[Regression] Air Quality

2023. 5. 7. 19:50

Main Conclusion

Time series analysis was conducted on Air Quality data and built predictive models for the variables 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', and 'PT08.S5'. To systematically understand the historical characteristics of the time series, the analysis was divied into univariate analysis and multivariate analysis. Based on these analyses, several models was constructed to estimate future time series values, and its performance was evaluated. In conclusion, the predictor variables exhibit a long-term equilibrium relationship, showing a generally mutual influence among them. Among these variables, only PT08.S1 was found not to Granger-cause the other variables.

Summary for Results by Analysis Procedures

Step01. Data Extraction

Missing Value & Duplication Inspection: The given data consists of a total of 9,357 entries with 13 columns during 2004-03-10 18:00:00 ~ 2005-04-04 14:00:00. Among these, the highest number of missing values was identified with 8,443 cases. The remaining columns exhibit missing values of either 366 cases or 1,639 cases. In terms of duplication, 'CO(GT)', 'NO2(GT)', 'C6H6(GT)', 'NMHC(GT)' columns exhibit high levels of duplication in that order.
Data Interpolation through Gaussian Process: The missing values were filled in using Gaussian interpolation. All columns except for NMHC(GT) satisfy null integrity. And only NMHC(GT) has 8,126 missing values. The reason Gaussian interpolation was used is to ensure the exisiting stattistical statbility, thereby preserving the time series characteristics.

Step02. Exploratory Data Analysis

Descriptive statistics: The time series unit is in hours, and it has verified that the count of weekly data is evenly distributed as 24*7, 168. Additionally, the time series characteristics of montly auto-correlation, heteroscedasticity, normality and stationary are described. Lastly, the cycle subseries of the time series are visualized hourly, monthly.
- Weekly description: count, max, min, mean, standard deviation
- Monthly description: auto-correlation, heteroscedasticity, normality, stationary
- Cycle subseries description: visualization about temporary seasonal series
Exploration for time series process: The fundamental approach to time series analysis involves distinguishing between deterministic processes and stochastics processes. Buling upon this, the robust nature of STL(Seasonal and Trend decomposition using Loess) is utlized to explore deterministic process. While UCM(Unobserved Component Model) is employed to investigate stochastic processes. Ultimately, this enables examination of the processes related to trend and seasonality.
- Deterministic process of time series features: STL
- Stochastic process of time series features: UCM

Step03. Univariate Time Series Characteristic Analysis

Stationary Analysis: Stationary refers to the property where the statistical characteristics of a time series remain consistent over time regardless of the lag. If stationary is not maintained, it become challengging to define the characteristics of the time series. Therefore, it's crucial initially to assess the stationary of a time series. To account for both difference and trend stationary, both the Augumented Dickey-Fuller (ADF) test and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test are utilized.
- Difference Stationary: ADF
- Trend Stationary: KPSS
Auto-Correlation/Covariance Analysis: The autocorrelation/autocovariance structure of a time series play a crucial role in time series analysis, as it ultimately determines the trend and seasonality of the time series. To assess this structure while maintaining the stationary property of the time series, the autocorrelation and autocovariance structure were visualized at various time intervals, including per time unit, monthly, quarterly, yearly.
- ACF and PACF: Yule-Walker Method
- Auto-Correlation/Covariance Structure: sample covariance method; ordinary least squares
Volatility Analysis: The statistical properties of stochastic process are primarily determined by their first and second moments. Typically, when analyzing autocorrelation structure, it is assumed that the population parameters of the first and second moments remain constant. Conversly, volatility analysis seeks to understand conditional volatility by considering time dependency in the second moment.
- GJR-GARCH(Generalized AutoRegressive Conditional Heteroskedasticity)
Regime Analysis: Regime analysis can understood as an extension of volatility analysis, where the time dependency of the second moment is defined by transition probabliities between regimes. It involves observing regime-specific durations and determining transition probabilities between regimes. In conclusion, it has been confirmed that there is no need to consider volatility for the pollutant variables 'PT08.S1(CO)', 'PT08.S2(NMHC)', 'PT08.S3(NOx)', 'PT08.S4(NO2)', 'PT08.S5(O3)'.
- MSM(Markov Switching Model)

Step04. Multivariate Time Series Characteristic Analysis

Cross-Covariance Analysis: To understand the covariance patterns on an hourly, weekly, monthly, monthly on year, analysis of covariance (ANCOVA) is conducted. This is done to identify key date factors that influence the time series characteristics.
- ANCOVA: Analysis of Covariance
Cointegration Analysis: To avoid spurious regression issues, cointegration relationship was explored in the time series. By johansen cointegration test, the cointegration rank has been determined as 4.
- Bivariate Cointegration Analysis: Augmented Engle-Granger Method
- Multivariate Cointegration Analysis: Johansen Cointegration Test
Principal Component Analysis(PCA): The first principal component to view the random variable for the given data from a different perspective is a set of the pollutants variables including 'NMHC(GT)'.; ['PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5']
- PCA for Stochastic Time Series Compoents
Dynamic Factor Analysis(DFA): As a key factor, along with the first principal component about results in PCA, 'CO(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)' are loaded into the common loadings of the first factor while 'T', 'RH' and 'AH' remain as unique loadings.

Step05. Predictive Modeling and Evaluation

Time Series Model Design: All modeling was conducted under the assumption that time series exhibit deterministic seasonality and stochastic trends. The purpose is to build and evaluate a time series model for stochastic trends with removed seasonality.
- Overall Model Specification
- Base Preprocessing for Forecasting Pollutants Variables
Time Series Model Evaluation and Forecast: The time series models were constructed into baseline and improved models, and the results of h-step forecast evaluations were presented.
- Baseline Explanation Model
  - Naive Forecast, ETS(AAN)
- Improvement Model
  - Predictor variable: pollutants: 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5'
  - Short-Term Forecast
    - Univariate: ARDL, SARIMAX, SVM
    - Multivariate: VARMAX[Reduced, Structural-Orthogonal Residual]
Impulse Response Analysis: Through Impulse Response Analysis (IRA), the potential tapering-off effects that can occur if there are long-term equilibrium relationships was explored to understand the characteristics of endogenous variables in the time series model. As a result, PT08.S1(CO) was found to not granger cause other pollutants.
- IR Analysis Model
  - Univariate Orthogonalized IRF: SARIMAX
  - Multivariate Orthogonalized IRF: VAR/VECM
- Granger Causality Analysis: VAR/VECM

Step06. Summary for Results by Analysis Procedures

Step07. Main Conclusion

Predictive Modeling and Evaluation

Impulse Response and Granger Causality Analysis

Univariate IRF: SARIMAX

endogenous variables: PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3), CO(GT), NMHC(GT), C6H6(GT), NOx(GT), NO2(GT), T, RH, AH
autoregressive order: 2
[IRF Train Period]: 2004-03-10 18:00:00 ~ 2004-05-01 00:00:00, 1231

Multivariate IRF: VAR/VECM

endogenous variables: PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)
cointegration exogenous variables: CO(GT), NMHC(GT), C6H6(GT), NOx(GT), NO2(GT)
exogenous variables: T, RH, AH
cointegration rank: 4
autoregressive order: 2
[Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
[Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73
[IRF Train Period]: 2004-03-10 18:00:00 ~ 2004-05-01 00:00:00, 1231

Granger Causality Analysis

PT08.S1(CO) does not Granger-cause PT08.S2(NMHC)
PT08.S2(NMHC) do Granger-cause PT08.S1(CO)

PT08.S1(CO) does not Granger-cause PT08.S3(NOx)
PT08.S3(NOx) do Granger-cause PT08.S1(CO)

PT08.S1(CO) does not Granger-cause PT08.S4(NO2)
PT08.S4(NO2) do Granger-cause PT08.S1(CO)

PT08.S1(CO) does not Granger-cause PT08.S5(O3)
PT08.S5(O3) do Granger-cause PT08.S1(CO)

PT08.S4(NO2) does not Granger-cause PT08.S3(NOx)
PT08.S3(NOx) do Granger-cause PT08.S4(NO2)

PT08.S5(O3) does not Granger-cause PT08.S1(CO)
PT08.S1(CO) do Granger-cause PT08.S5(O3)

PT08.S5(O3) does not Granger-cause PT08.S4(NO2)
PT08.S4(NO2) do Granger-cause PT08.S5(O3)

	By cause	Effect	Causality type	Test statistic	Critical value	p-value	df	H0: Null hypothesis	Test result	Granger Causality	Instantaneous Causality
0	PT08.S1(CO)	PT08.S1(CO)	Granger causality F-test	242.976132	2.606392	8.685386e-149	(3, 5990)	PT08.S1(CO) does not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
6	PT08.S2(NMHC)	PT08.S1(CO)	Granger causality F-test	38.390892	2.606392	1.446181e-24	(3, 5990)	PT08.S2(NMHC) does not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
7	PT08.S3(NOx)	PT08.S1(CO)	Granger causality F-test	11.514925	2.606392	1.593106e-07	(3, 5990)	PT08.S3(NOx) does not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
8	PT08.S4(NO2)	PT08.S1(CO)	Granger causality F-test	29.948117	2.606392	3.278482e-19	(3, 5990)	PT08.S4(NO2) does not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
9	PT08.S5(O3)	PT08.S1(CO)	Granger causality F-test	2.075985	2.606392	1.011516e-01	(3, 5990)	PT08.S5(O3) does not Granger-cause PT08.S1(CO)	fail to reject H_0 at 5% significance level.	False	-
5	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S1(CO)	Granger causality F-test	76.184574	1.753786	1.463578e-174	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
16	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	PT08.S1(CO)	Granger causality F-test	94.129400	1.881443	7.445732e-165	(9, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
17	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\']	PT08.S1(CO)	Granger causality F-test	16.083500	1.881443	2.346265e-26	(9, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
10	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	PT08.S1(CO)	Granger causality F-test	23.297272	2.100103	2.375558e-27	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
18	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S1(CO)	Granger causality F-test	84.093331	1.881443	1.045150e-147	(9, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
11	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	PT08.S1(CO)	Granger causality F-test	122.328522	2.100103	2.424444e-146	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
12	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	PT08.S1(CO)	Granger causality F-test	19.495824	2.100103	1.190212e-22	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
19	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S1(CO)	Granger causality F-test	16.583265	1.881443	2.896168e-27	(9, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
13	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	PT08.S1(CO)	Granger causality F-test	23.319128	2.100103	2.232157e-27	(6, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
14	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\']	PT08.S1(CO)	Granger causality F-test	7.744475	2.100103	2.576535e-08	(6, 5990)	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
15	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S1(CO)	Granger causality F-test	16.021190	2.100103	2.286888e-18	(6, 5990)	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S1(CO)	reject H_0 at 5% significance level.	True	-
21	PT08.S1(CO)	PT08.S2(NMHC)	Granger causality F-test	1.322332	2.606392	2.651576e-01	(3, 5990)	PT08.S1(CO) does not Granger-cause PT08.S2(NMHC)	fail to reject H_0 at 5% significance level.	False	-
1	PT08.S2(NMHC)	PT08.S2(NMHC)	Granger causality F-test	0.299041	2.606392	8.261201e-01	(3, 5990)	PT08.S2(NMHC) does not Granger-cause PT08.S2(NMHC)	fail to reject H_0 at 5% significance level.	False	-
22	PT08.S3(NOx)	PT08.S2(NMHC)	Granger causality F-test	142.757856	2.606392	2.396742e-89	(3, 5990)	PT08.S3(NOx) does not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
23	PT08.S4(NO2)	PT08.S2(NMHC)	Granger causality F-test	6.902389	2.606392	1.230777e-04	(3, 5990)	PT08.S4(NO2) does not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
24	PT08.S5(O3)	PT08.S2(NMHC)	Granger causality F-test	3.178949	2.606392	2.301372e-02	(3, 5990)	PT08.S5(O3) does not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
20	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S2(NMHC)	Granger causality F-test	49.673247	1.753786	5.027458e-114	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
31	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	PT08.S2(NMHC)	Granger causality F-test	64.258682	1.881443	3.394356e-113	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
32	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\']	PT08.S2(NMHC)	Granger causality F-test	50.931122	1.881443	1.511647e-89	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
25	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\']	PT08.S2(NMHC)	Granger causality F-test	72.962868	2.100103	3.747497e-88	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
33	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S2(NMHC)	Granger causality F-test	4.553057	1.881443	5.300025e-06	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
26	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\']	PT08.S2(NMHC)	Granger causality F-test	3.862469	2.100103	7.516101e-04	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
27	[\'PT08.S1(CO)\', \'PT08.S5(O3)\']	PT08.S2(NMHC)	Granger causality F-test	3.013720	2.100103	6.081282e-03	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
34	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S2(NMHC)	Granger causality F-test	61.976621	1.881443	3.583655e-109	(9, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
28	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	PT08.S2(NMHC)	Granger causality F-test	90.150101	2.100103	1.098180e-108	(6, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
29	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\']	PT08.S2(NMHC)	Granger causality F-test	73.899580	2.100103	2.800282e-89	(6, 5990)	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
30	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S2(NMHC)	Granger causality F-test	5.246220	2.100103	2.120826e-05	(6, 5990)	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S2(NMHC)	reject H_0 at 5% significance level.	True	-
36	PT08.S1(CO)	PT08.S3(NOx)	Granger causality F-test	0.552846	2.606392	6.462112e-01	(3, 5990)	PT08.S1(CO) does not Granger-cause PT08.S3(NOx)	fail to reject H_0 at 5% significance level.	False	-
37	PT08.S2(NMHC)	PT08.S3(NOx)	Granger causality F-test	21.797713	2.606392	4.908031e-14	(3, 5990)	PT08.S2(NMHC) does not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
2	PT08.S3(NOx)	PT08.S3(NOx)	Granger causality F-test	535.641656	2.606392	2.171038e-308	(3, 5990)	PT08.S3(NOx) does not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
38	PT08.S4(NO2)	PT08.S3(NOx)	Granger causality F-test	1.062097	2.606392	3.638691e-01	(3, 5990)	PT08.S4(NO2) does not Granger-cause PT08.S3(NOx)	fail to reject H_0 at 5% significance level.	False	-
39	PT08.S5(O3)	PT08.S3(NOx)	Granger causality F-test	4.458826	2.606392	3.914461e-03	(3, 5990)	PT08.S5(O3) does not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
35	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S3(NOx)	Granger causality F-test	53.823814	1.753786	1.145878e-123	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
46	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	PT08.S3(NOx)	Granger causality F-test	31.062981	1.881443	1.130043e-53	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
47	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	PT08.S3(NOx)	Granger causality F-test	13.106776	1.881443	5.800537e-21	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
40	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\']	PT08.S3(NOx)	Granger causality F-test	12.417211	2.100103	5.968478e-14	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
48	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S3(NOx)	Granger causality F-test	2.415664	1.881443	9.829935e-03	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
41	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\']	PT08.S3(NOx)	Granger causality F-test	0.837058	2.100103	5.410050e-01	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S3(NOx)	fail to reject H_0 at 5% significance level.	False	-
42	[\'PT08.S1(CO)\', \'PT08.S5(O3)\']	PT08.S3(NOx)	Granger causality F-test	3.241024	2.100103	3.508490e-03	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
49	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S3(NOx)	Granger causality F-test	22.849300	1.881443	1.086013e-38	(9, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
43	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	PT08.S3(NOx)	Granger causality F-test	27.359396	2.100103	2.231248e-32	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
44	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	PT08.S3(NOx)	Granger causality F-test	14.794095	2.100103	7.362809e-17	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
45	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\']	PT08.S3(NOx)	Granger causality F-test	2.831712	2.100103	9.387131e-03	(6, 5990)	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S3(NOx)	reject H_0 at 5% significance level.	True	-
51	PT08.S1(CO)	PT08.S4(NO2)	Granger causality F-test	2.039496	2.606392	1.061067e-01	(3, 5990)	PT08.S1(CO) does not Granger-cause PT08.S4(NO2)	fail to reject H_0 at 5% significance level.	False	-
52	PT08.S2(NMHC)	PT08.S4(NO2)	Granger causality F-test	52.923585	2.606392	9.370835e-34	(3, 5990)	PT08.S2(NMHC) does not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
53	PT08.S3(NOx)	PT08.S4(NO2)	Granger causality F-test	43.001065	2.606392	1.740571e-27	(3, 5990)	PT08.S3(NOx) does not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
3	PT08.S4(NO2)	PT08.S4(NO2)	Granger causality F-test	30.517211	2.606392	1.426956e-19	(3, 5990)	PT08.S4(NO2) does not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
54	PT08.S5(O3)	PT08.S4(NO2)	Granger causality F-test	0.128394	2.606392	9.432819e-01	(3, 5990)	PT08.S5(O3) does not Granger-cause PT08.S4(NO2)	fail to reject H_0 at 5% significance level.	False	-
50	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\']	PT08.S4(NO2)	Granger causality F-test	17.302838	1.753786	4.248405e-37	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
61	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	PT08.S4(NO2)	Granger causality F-test	22.805736	1.881443	1.304286e-38	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
62	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	PT08.S4(NO2)	Granger causality F-test	17.947715	1.881443	9.511340e-30	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
55	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\']	PT08.S4(NO2)	Granger causality F-test	26.550076	2.100103	2.239768e-31	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
63	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\']	PT08.S4(NO2)	Granger causality F-test	15.706993	1.881443	1.133385e-25	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
56	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\']	PT08.S4(NO2)	Granger causality F-test	21.614024	2.100103	2.869846e-25	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
57	[\'PT08.S1(CO)\', \'PT08.S5(O3)\']	PT08.S4(NO2)	Granger causality F-test	1.244474	2.100103	2.800001e-01	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S4(NO2)	fail to reject H_0 at 5% significance level.	False	-
64	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\']	PT08.S4(NO2)	Granger causality F-test	22.987170	1.881443	6.082898e-39	(9, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
58	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	PT08.S4(NO2)	Granger causality F-test	34.079614	2.100103	1.089561e-40	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
59	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	PT08.S4(NO2)	Granger causality F-test	26.805440	2.100103	1.081801e-31	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
60	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\']	PT08.S4(NO2)	Granger causality F-test	22.897668	2.100103	7.415814e-27	(6, 5990)	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause PT08.S4(NO2)	reject H_0 at 5% significance level.	True	-
66	PT08.S1(CO)	PT08.S5(O3)	Granger causality F-test	0.988534	2.606392	3.970351e-01	(3, 5990)	PT08.S1(CO) does not Granger-cause PT08.S5(O3)	fail to reject H_0 at 5% significance level.	False	-
67	PT08.S2(NMHC)	PT08.S5(O3)	Granger causality F-test	39.451808	2.606392	3.076235e-25	(3, 5990)	PT08.S2(NMHC) does not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
68	PT08.S3(NOx)	PT08.S5(O3)	Granger causality F-test	12.606204	2.606392	3.266968e-08	(3, 5990)	PT08.S3(NOx) does not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
69	PT08.S4(NO2)	PT08.S5(O3)	Granger causality F-test	6.255051	2.606392	3.097984e-04	(3, 5990)	PT08.S4(NO2) does not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
4	PT08.S5(O3)	PT08.S5(O3)	Granger causality F-test	319.312567	2.606392	2.487520e-192	(3, 5990)	PT08.S5(O3) does not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
65	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	PT08.S5(O3)	Granger causality F-test	48.150887	1.753786	1.790279e-110	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
76	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	PT08.S5(O3)	Granger causality F-test	15.373700	1.881443	4.565604e-25	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
77	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	PT08.S5(O3)	Granger causality F-test	60.731576	1.881443	5.676010e-107	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
70	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\']	PT08.S5(O3)	Granger causality F-test	22.194135	2.100103	5.500853e-26	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
78	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	PT08.S5(O3)	Granger causality F-test	7.353858	1.881443	9.811750e-11	(9, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
71	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\']	PT08.S5(O3)	Granger causality F-test	7.055542	2.100103	1.680113e-07	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
72	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\']	PT08.S5(O3)	Granger causality F-test	3.285629	2.100103	3.146561e-03	(6, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
79	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	PT08.S5(O3)	Granger causality F-test	42.089433	1.881443	1.150750e-73	(9, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
73	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	PT08.S5(O3)	Granger causality F-test	20.895980	2.100103	2.216207e-24	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
74	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	PT08.S5(O3)	Granger causality F-test	58.630591	2.100103	8.230165e-71	(6, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
75	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	PT08.S5(O3)	Granger causality F-test	10.167651	2.100103	3.217170e-11	(6, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause PT08.S5(O3)	reject H_0 at 5% significance level.	True	-
180	PT08.S5(O3)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	3.697339	1.753786	1.389086e-05	(12, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
181	PT08.S4(NO2)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	11.949458	1.753786	2.566745e-24	(12, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
151	PT08.S4(NO2)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	14.970390	1.881443	2.461643e-24	(9, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
152	PT08.S5(O3)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	4.739396	1.881443	2.630749e-06	(9, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
150	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	9.811097	1.605573	1.298403e-27	(18, 5990)	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
182	PT08.S3(NOx)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	44.192180	1.753786	3.351272e-101	(12, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
154	PT08.S3(NOx)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	57.248873	1.881443	8.396912e-101	(9, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
155	PT08.S5(O3)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	3.353334	1.881443	4.182664e-04	(9, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
153	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	30.916547	1.605573	1.274714e-101	(18, 5990)	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
157	PT08.S3(NOx)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	56.315310	1.881443	3.821697e-99	(9, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
158	PT08.S4(NO2)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	13.145421	1.881443	4.939876e-21	(9, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
156	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	[PT08.S1(CO), PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	39.097140	1.605573	8.096776e-130	(18, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
81	PT08.S3(NOx)	[PT08.S1(CO), PT08.S2(NMHC)]	Granger causality F-test	82.017468	2.100103	5.250221e-99	(6, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC)]	reject H_0 at 5% significance level.	True	-
82	PT08.S4(NO2)	[PT08.S1(CO), PT08.S2(NMHC)]	Granger causality F-test	16.953421	2.100103	1.628265e-19	(6, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC)]	reject H_0 at 5% significance level.	True	-
83	PT08.S5(O3)	[PT08.S1(CO), PT08.S2(NMHC)]	Granger causality F-test	4.760208	2.100103	7.553233e-05	(6, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S1(CO), PT08.S2(NMHC)]	reject H_0 at 5% significance level.	True	-
80	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S2(NMHC)]	Granger causality F-test	38.794502	1.605573	8.773917e-129	(18, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S2(NMHC)]	reject H_0 at 5% significance level.	True	-
84	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	[PT08.S1(CO), PT08.S2(NMHC)]	Granger causality F-test	55.255555	1.753786	5.585312e-127	(12, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S1(CO), PT08.S2(NMHC)]	reject H_0 at 5% significance level.	True	-
85	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S2(NMHC)]	Granger causality F-test	44.112366	1.753786	5.160544e-101	(12, 5990)	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S2(NMHC)]	reject H_0 at 5% significance level.	True	-
86	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S2(NMHC)]	Granger causality F-test	10.744076	1.753786	1.812578e-21	(12, 5990)	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S2(NMHC)]	reject H_0 at 5% significance level.	True	-
183	PT08.S2(NMHC)	[PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	20.131969	1.753786	6.863686e-44	(12, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
160	PT08.S2(NMHC)	[PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	24.181136	1.881443	4.019454e-41	(9, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
161	PT08.S5(O3)	[PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	3.390101	1.881443	3.675082e-04	(9, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
159	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	13.990940	1.605573	3.297766e-42	(18, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
163	PT08.S2(NMHC)	[PT08.S1(CO), PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	17.853970	1.881443	1.409287e-29	(9, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S1(CO), PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
164	PT08.S4(NO2)	[PT08.S1(CO), PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	11.652685	1.881443	2.405236e-18	(9, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S1(CO), PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
162	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	[PT08.S1(CO), PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	43.618536	1.605573	3.359796e-145	(18, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S1(CO), PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
88	PT08.S2(NMHC)	[PT08.S1(CO), PT08.S3(NOx)]	Granger causality F-test	22.610704	2.100103	1.679418e-26	(6, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S1(CO), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
89	PT08.S4(NO2)	[PT08.S1(CO), PT08.S3(NOx)]	Granger causality F-test	16.301834	2.100103	1.032657e-18	(6, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S1(CO), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
90	PT08.S5(O3)	[PT08.S1(CO), PT08.S3(NOx)]	Granger causality F-test	4.800594	2.100103	6.800829e-05	(6, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S1(CO), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
87	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S3(NOx)]	Granger causality F-test	45.020610	1.605573	6.122018e-150	(18, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
91	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	[PT08.S1(CO), PT08.S3(NOx)]	Granger causality F-test	62.937316	1.753786	1.261257e-144	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S1(CO), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
92	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S3(NOx)]	Granger causality F-test	13.964728	1.753786	4.132860e-29	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
93	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S3(NOx)]	Granger causality F-test	10.548064	1.753786	5.246873e-21	(12, 5990)	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
166	PT08.S2(NMHC)	[PT08.S1(CO), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	26.737321	1.881443	8.676974e-46	(9, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S1(CO), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
167	PT08.S3(NOx)	[PT08.S1(CO), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	18.682608	1.881443	4.356107e-31	(9, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S1(CO), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
165	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	[PT08.S1(CO), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	18.360429	1.605573	1.332973e-57	(18, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S1(CO), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
95	PT08.S2(NMHC)	[PT08.S1(CO), PT08.S4(NO2)]	Granger causality F-test	35.097800	2.100103	6.019555e-42	(6, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S1(CO), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
96	PT08.S3(NOx)	[PT08.S1(CO), PT08.S4(NO2)]	Granger causality F-test	24.678203	2.100103	4.644502e-29	(6, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S1(CO), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
97	PT08.S5(O3)	[PT08.S1(CO), PT08.S4(NO2)]	Granger causality F-test	1.318931	2.100103	2.446962e-01	(6, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S1(CO), PT08.S4(NO2)]	fail to reject H_0 at 5% significance level.	False	-
94	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S4(NO2)]	Granger causality F-test	16.618862	1.605573	1.842573e-51	(18, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
98	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	[PT08.S1(CO), PT08.S4(NO2)]	Granger causality F-test	24.198090	1.753786	1.177786e-53	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S1(CO), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
99	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S4(NO2)]	Granger causality F-test	18.035714	1.753786	7.412041e-39	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
100	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\']	[PT08.S1(CO), PT08.S4(NO2)]	Granger causality F-test	14.041399	1.753786	2.712284e-29	(12, 5990)	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S1(CO), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
102	PT08.S2(NMHC)	[PT08.S1(CO), PT08.S5(O3)]	Granger causality F-test	25.512310	2.100103	4.311451e-30	(6, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S1(CO), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
103	PT08.S3(NOx)	[PT08.S1(CO), PT08.S5(O3)]	Granger causality F-test	10.227499	2.100103	2.723753e-11	(6, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S1(CO), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
104	PT08.S4(NO2)	[PT08.S1(CO), PT08.S5(O3)]	Granger causality F-test	16.801326	2.100103	2.506390e-19	(6, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S1(CO), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
101	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	[PT08.S1(CO), PT08.S5(O3)]	Granger causality F-test	49.970543	1.605573	1.485641e-166	(18, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S1(CO), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
105	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	[PT08.S1(CO), PT08.S5(O3)]	Granger causality F-test	15.694140	1.753786	3.041488e-33	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S1(CO), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
106	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	[PT08.S1(CO), PT08.S5(O3)]	Granger causality F-test	64.790015	1.753786	7.522899e-149	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S1(CO), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
107	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	[PT08.S1(CO), PT08.S5(O3)]	Granger causality F-test	14.501687	1.753786	2.160320e-30	(12, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S1(CO), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
184	PT08.S1(CO)	[PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	2.206276	1.753786	9.298224e-03	(12, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
169	PT08.S1(CO)	[PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	2.662247	1.881443	4.419203e-03	(9, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
170	PT08.S5(O3)	[PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	3.007388	1.881443	1.387469e-03	(9, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
168	[\'PT08.S1(CO)\', \'PT08.S5(O3)\']	[PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	2.935470	1.605573	2.943222e-05	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
172	PT08.S1(CO)	[PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	2.294625	1.881443	1.440787e-02	(9, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
173	PT08.S4(NO2)	[PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	8.009162	1.881443	7.080145e-12	(9, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
171	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\']	[PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	4.806738	1.605573	7.435402e-11	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
109	PT08.S1(CO)	[PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	3.068935	2.100103	5.324794e-03	(6, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
110	PT08.S4(NO2)	[PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	9.091622	2.100103	6.355526e-10	(6, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
111	PT08.S5(O3)	[PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	4.011977	2.100103	5.153055e-04	(6, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
108	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\']	[PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	5.142349	1.605573	6.366177e-12	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
112	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\']	[PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	5.697091	1.753786	7.455053e-10	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
113	[\'PT08.S1(CO)\', \'PT08.S5(O3)\']	[PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	3.252565	1.753786	1.077941e-04	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
114	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\']	[PT08.S2(NMHC), PT08.S3(NOx)]	Granger causality F-test	6.711379	1.753786	4.008284e-12	(12, 5990)	[\'PT08.S4(NO2)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S3(NOx)]	reject H_0 at 5% significance level.	True	-
175	PT08.S1(CO)	[PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	1.395341	1.881443	1.839347e-01	(9, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	fail to reject H_0 at 5% significance level.	False	-
176	PT08.S3(NOx)	[PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	52.342075	1.881443	4.559191e-92	(9, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
174	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\']	[PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	26.954125	1.605573	8.274599e-88	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
116	PT08.S1(CO)	[PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	1.538218	2.100103	1.612991e-01	(6, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2)]	fail to reject H_0 at 5% significance level.	False	-
117	PT08.S3(NOx)	[PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	73.385337	2.100103	1.162926e-88	(6, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
118	PT08.S5(O3)	[PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	2.064536	2.100103	5.403727e-02	(6, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2)]	fail to reject H_0 at 5% significance level.	False	-
115	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\']	[PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	26.836549	1.605573	2.132832e-87	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
119	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\']	[PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	37.753857	1.753786	5.186991e-86	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
120	[\'PT08.S1(CO)\', \'PT08.S5(O3)\']	[PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	2.616769	1.753786	1.744625e-03	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
121	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\']	[PT08.S2(NMHC), PT08.S4(NO2)]	Granger causality F-test	38.312533	1.753786	2.464349e-87	(12, 5990)	[\'PT08.S3(NOx)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
123	PT08.S1(CO)	[PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	1.143730	2.100103	3.339180e-01	(6, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S2(NMHC), PT08.S5(O3)]	fail to reject H_0 at 5% significance level.	False	-
124	PT08.S3(NOx)	[PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	75.963406	2.100103	9.292988e-92	(6, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
125	PT08.S4(NO2)	[PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	7.066363	2.100103	1.631540e-07	(6, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
122	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	[PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	35.354601	1.605573	5.643814e-117	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
126	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\']	[PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	38.886015	1.753786	1.082449e-88	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
127	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\']	[PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	3.869675	1.753786	6.170090e-06	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
128	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\']	[PT08.S2(NMHC), PT08.S5(O3)]	Granger causality F-test	49.798629	1.753786	2.565633e-114	(12, 5990)	[\'PT08.S3(NOx)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S2(NMHC), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
178	PT08.S1(CO)	[PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	1.501865	1.881443	1.408765e-01	(9, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	fail to reject H_0 at 5% significance level.	False	-
179	PT08.S2(NMHC)	[PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	25.315687	1.881443	3.411476e-43	(9, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
177	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\']	[PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	13.804226	1.605573	1.493988e-41	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\'] do not Granger-cause [PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
130	PT08.S1(CO)	[PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	1.768309	2.100103	1.014136e-01	(6, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S3(NOx), PT08.S4(NO2)]	fail to reject H_0 at 5% significance level.	False	-
131	PT08.S2(NMHC)	[PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	29.753911	2.100103	2.429565e-35	(6, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
132	PT08.S5(O3)	[PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	2.734038	2.100103	1.181956e-02	(6, 5990)	PT08.S5(O3) does not Granger-cause [PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
129	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	[PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	13.045242	1.605573	6.898592e-39	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
133	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\']	[PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	15.745941	1.753786	2.286051e-33	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\'] do not Granger-cause [PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
134	[\'PT08.S1(CO)\', \'PT08.S5(O3)\']	[PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	2.853525	1.753786	6.333739e-04	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
135	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\']	[PT08.S3(NOx), PT08.S4(NO2)]	Granger causality F-test	16.988859	1.753786	2.405278e-36	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S5(O3)\'] do not Granger-cause [PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	True	-
137	PT08.S1(CO)	[PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	0.758355	2.100103	6.026898e-01	(6, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S3(NOx), PT08.S5(O3)]	fail to reject H_0 at 5% significance level.	False	-
138	PT08.S2(NMHC)	[PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	21.837842	2.100103	1.517333e-25	(6, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
139	PT08.S4(NO2)	[PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	3.183756	2.100103	4.033080e-03	(6, 5990)	PT08.S4(NO2) does not Granger-cause [PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
136	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	[PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	32.967278	1.605573	9.876680e-109	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
140	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\']	[PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	12.465452	1.753786	1.531878e-25	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\'] do not Granger-cause [PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
141	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\']	[PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	1.786970	1.753786	4.451629e-02	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
142	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\']	[PT08.S3(NOx), PT08.S5(O3)]	Granger causality F-test	31.224285	1.753786	1.763191e-70	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S4(NO2)\'] do not Granger-cause [PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
144	PT08.S1(CO)	[PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	1.667514	2.100103	1.246490e-01	(6, 5990)	PT08.S1(CO) does not Granger-cause [PT08.S4(NO2), PT08.S5(O3)]	fail to reject H_0 at 5% significance level.	False	-
145	PT08.S2(NMHC)	[PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	37.730640	2.100103	3.388744e-45	(6, 5990)	PT08.S2(NMHC) does not Granger-cause [PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
146	PT08.S3(NOx)	[PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	24.046453	2.100103	2.810268e-28	(6, 5990)	PT08.S3(NOx) does not Granger-cause [PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
143	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	[PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	16.449647	1.605573	7.276024e-51	(18, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
147	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\']	[PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	20.214069	1.753786	4.358684e-44	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S2(NMHC)\'] do not Granger-cause [PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
148	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\']	[PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	12.463419	1.753786	1.548994e-25	(12, 5990)	[\'PT08.S1(CO)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
149	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\']	[PT08.S4(NO2), PT08.S5(O3)]	Granger causality F-test	23.473280	1.753786	6.473219e-52	(12, 5990)	[\'PT08.S2(NMHC)\', \'PT08.S3(NOx)\'] do not Granger-cause [PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	True	-
189	PT08.S5(O3)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	Instantaneous causality Wald-test	337.439976	9.487729	9.027617e-72	4	PT08.S5(O3) does not instantaneously cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2)]	reject H_0 at 5% significance level.	-	True
188	PT08.S4(NO2)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	Instantaneous causality Wald-test	217.970810	9.487729	5.123598e-46	4	PT08.S4(NO2) does not instantaneously cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S3(NOx), PT08.S5(O3)]	reject H_0 at 5% significance level.	-	True
187	PT08.S3(NOx)	[PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	Instantaneous causality Wald-test	460.331063	9.487729	2.536898e-98	4	PT08.S3(NOx) does not instantaneously cause [PT08.S1(CO), PT08.S2(NMHC), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	-	True
186	PT08.S2(NMHC)	[PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	Instantaneous causality Wald-test	486.285247	9.487729	6.196463e-104	4	PT08.S2(NMHC) does not instantaneously cause [PT08.S1(CO), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	-	True
185	PT08.S1(CO)	[PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	Instantaneous causality Wald-test	351.004087	9.487729	1.064586e-74	4	PT08.S1(CO) does not instantaneously cause [PT08.S2(NMHC), PT08.S3(NOx), PT08.S4(NO2), PT08.S5(O3)]	reject H_0 at 5% significance level.	-	True

Time Series Model Evaluation

Baseline Explanation Model

Naive Forecast, ETS(AAN)
- Target(All, 13): 'PT08.S1(CO)', 'PT08.S2(NMHC)', 'PT08.S3(NOx)', 'PT08.S4(NO2)', 'PT08.S5(O3)', 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)', 'T', 'RH', 'AH'
- h-step forecast evaluation
- [Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
- [Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73

Model	Naive																														ETS AAdN
Domain	Train															Test															Train														Test
Info	start	end	model	total	sst	ssr	sse	ssr/sst	sse/sst	ssr/sse	mst	msr	mse	rmse	mape	start	end	model	total	sst	ssr	sse	ssr/sst	sse/sst	ssr/sse	mst	msr	mse	rmse	mape	start	end	total	sst	ssr	sse	ssr/sst	sse/sst	ssr/sse	mst	msr	mse	rmse	mape	start	end	total	sst	ssr	sse	ssr/sst	sse/sst	ssr/sse	mst	msr	mse	rmse	mape
CO(GT)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	952.01381	952.551014	472.575238	1.000564	0.496395	2.01566	0.82283	952.551014	0.408448	0.638824	17.320883	2004-04-28	2004-05-01	Naive	73	952.01381	3.052784	80.186239	0.003207	0.084228	0.038071	0.82283	3.052784	0.856304	1.048066	2.18195	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	952.01381	952.954703	472.597244	1.000988	0.496418	2.01642	0.82283	952.954703	0.408467	0.638839	17.321287	2004-04-28	2004-05-01	73	61.653863	18.527789	80.181143	0.300513	1.300505	0.231074	0.856304	18.527789	0.856297	1.048032	2.182516
PT08.S1(CO)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	37329666.834193	37329601.532309	12421823.909175	0.999998	0.33276	3.005163	32264.189139	37329601.532309	10736.234861	103.571056	2.06029	2004-04-28	2004-05-01	Naive	73	37329666.834193	6469.483204	2978327.785717	0.000173	0.079784	0.002172	32264.189139	6469.483204	18938.320225	201.98765	2.004873	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	37329666.834193	37336579.645433	12422778.357097	1.000185	0.332786	3.005494	32264.189139	37336579.645433	10737.057413	103.575035	2.065533	2004-04-28	2004-05-01	73	1363559.056179	1614370.899647	2977898.411039	1.183939	2.183916	0.542118	18938.320225	1614370.899647	18937.882121	201.97309	2.003703
NMHC(GT)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	21597542.259443	21643014.400826	10580453.19625	1.002105	0.489892	2.045566	18666.847242	21643014.400826	9144.662762	95.586785	3.521068	2004-04-28	2004-05-01	Naive	73	21597542.259443	412474.657532	1960016.119058	0.019098	0.090752	0.210445	18666.847242	412474.657532	25530.259559	163.85828	4.493315	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	21597542.259443	21620296.990207	10583569.292906	1.001054	0.490036	2.042817	18666.847242	21620296.990207	9147.397913	95.60086	3.520907	2004-04-28	2004-05-01	73	1838178.688282	121729.02287	1959896.178863	0.066223	1.066216	0.06211	25530.259559	121729.02287	25530.099417	163.853266	4.494018
C6H6(GT)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	32446.767948	32454.011441	13750.187331	1.000223	0.423777	2.36026	28.043879	32454.011441	11.884298	3.445879	4.924125	2004-04-28	2004-05-01	Naive	73	32446.767948	910.434266	1852.531235	0.028059	0.057094	0.491454	28.043879	910.434266	22.320845	5.037573	2.563734	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	32446.767948	32456.543488	13750.944468	1.000301	0.4238	2.360314	28.043879	32456.543488	11.884951	3.445974	4.924325	2004-04-28	2004-05-01	73	1607.100815	245.334122	1852.418523	0.152656	1.152646	0.13244	22.320845	245.334122	22.320617	5.03742	2.563929
PT08.S2(NMHC)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	39472603.176647	39463600.686054	13978758.389615	0.999772	0.354138	2.823112	34116.338096	39463600.686054	12081.845616	109.870226	3.318938	2004-04-28	2004-05-01	Naive	73	39472603.176647	1680521.102278	1469868.10471	0.042574	0.037238	1.143314	34116.338096	1680521.102278	18994.399669	141.898483	2.954736	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	39472603.176647	39472289.139354	13984909.452211	0.999992	0.354294	2.822492	34116.338096	39472289.139354	12087.154238	109.894397	3.319558	2004-04-28	2004-05-01	73	1367596.776148	102180.939834	1469753.648307	0.074716	1.074698	0.069522	18994.399669	102180.939834	18994.065414	141.892958	2.954923
NOx(GT)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	3560007.78425	3560228.362376	1590908.257933	1.000062	0.446883	2.237859	3076.929805	3560228.362376	1375.028492	37.065366	3.012007	2004-04-28	2004-05-01	Naive	73	3560007.78425	756.619486	238699.479019	0.000213	0.06705	0.00317	3076.929805	756.619486	2405.954339	57.182654	0.988974	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	3560007.78425	3536970.879439	1592098.63543	0.993529	0.447218	2.221578	3076.929805	3536970.879439	1376.056657	37.07923	3.003566	2004-04-28	2004-05-01	73	173228.712409	67124.454007	240351.129963	0.38749	1.387479	0.279277	2405.954339	67124.454007	2405.926056	57.380147	0.992285
PT08.S3(NOx)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	42892614.422674	42916057.572883	11252537.815437	1.000547	0.262342	3.8139	37072.2683	42916057.572883	9725.476366	98.575948	6.180128	2004-04-28	2004-05-01	Naive	73	42892614.422674	2614336.554891	724128.988102	0.060951	0.016882	3.610319	37072.2683	2614336.554891	8528.843129	99.597064	0.483034	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	42892614.422674	42958140.960404	11253185.294241	1.001528	0.262357	3.817421	37072.2683	42958140.960404	9725.988093	98.578784	6.180603	2004-04-28	2004-05-01	73	614076.705292	109857.568531	723910.81941	0.178899	1.178861	0.151756	8528.843129	109857.568531	8528.517426	99.582059	0.483035
NO2(GT)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	512557.628272	512481.325455	202092.401412	0.999851	0.394282	2.535876	443.005729	512481.325455	174.668826	13.210544	3.282934	2004-04-28	2004-05-01	Naive	73	512557.628272	14975.63331	18032.584565	0.029217	0.035182	0.830476	443.005729	14975.63331	219.010147	15.716924	8.176079	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	512557.628272	491611.511613	200763.614401	0.959134	0.39169	2.448708	443.005729	491611.511613	173.520837	13.167042	3.414677	2004-04-28	2004-05-01	73	15768.730578	1209.220989	16977.628126	0.076685	1.076664	0.071224	219.010147	1209.220989	219.005692	15.250254	7.337192
PT08.S4(NO2)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	53774910.490193	53772138.304848	20964867.878683	0.999948	0.389863	2.564869	46477.882878	53772138.304848	18119.989466	134.552504	4.563112	2004-04-28	2004-05-01	Naive	73	53774910.490193	950965.018231	4596426.807399	0.017684	0.085475	0.206892	46477.882878	950965.018231	34548.793047	250.92778	1.586831	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	53774910.490193	53317104.312277	20969437.771569	0.991487	0.389948	2.54261	46477.882878	53317104.312277	18123.929093	134.567168	4.63731	2004-04-28	2004-05-01	73	2487513.099357	2175054.00871	4662501.182581	0.874389	1.874362	0.466499	34548.793047	2175054.00871	34547.877459	252.724908	1.562477
PT08.S5(O3)	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	111778618.757775	111779298.311131	25473412.186856	1.000006	0.227892	4.388077	96610.733585	111779298.311131	22016.778022	148.316436	2.161779	2004-04-28	2004-05-01	Naive	73	111778618.757775	463604.041014	8318074.124279	0.004148	0.074416	0.055735	96610.733585	463604.041014	49276.386463	337.559211	1.246199	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	111778618.757775	111784511.268927	25499165.61918	1.000053	0.228122	4.38385	96610.733585	111784511.268927	22039.016001	148.391391	2.163942	2004-04-28	2004-05-01	73	3547899.825336	4769478.210775	8317328.740873	1.34431	2.344296	0.573439	49276.386463	4769478.210775	49275.701833	337.544086	1.24628
T	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	14478.410099	14483.396179	1150.001763	1.000344	0.079429	12.594238	12.513751	14483.396179	0.993894	0.996541	3.046411	2004-04-28	2004-05-01	Naive	73	14478.410099	1228.904351	389.831062	0.084878	0.026925	3.152402	12.513751	1228.904351	5.296909	2.310877	0.847462	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	14478.410099	15329.10426	1110.44043	1.058756	0.076696	13.804526	12.513751	15329.10426	0.959753	0.979249	3.099109	2004-04-28	2004-05-01	73	381.377482	32.870467	410.825195	0.086189	1.077214	0.080011	5.296909	32.870467	5.273289	2.372286	0.641351
RH	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	160435.204951	160336.131853	19916.41329	0.999382	0.12414	8.050452	138.664827	160336.131853	17.213529	4.147165	1.473727	2004-04-28	2004-05-01	Naive	73	160435.204951	11669.011393	29221.10802	0.072733	0.182137	0.399335	138.664827	11669.011393	145.912831	20.007227	6.707568	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	160435.204951	167371.766979	19821.190039	1.043236	0.123546	8.444083	138.664827	167371.766979	17.131429	4.137239	1.424345	2004-04-28	2004-05-01	73	10505.723806	17697.983183	28158.598116	1.684604	2.68031	0.628511	145.912831	17697.983183	145.29104	19.640118	6.476134
AH	2004-03-10 18:00:00	2004-04-27 23:00:00	Naive	1158	27.198789	27.204078	1.737284	1.000194	0.063874	15.658966	0.023508	27.204078	0.001502	0.038733	1.280164	2004-04-28	2004-05-01	Naive	73	27.198789	0.000389	8.432672	0.000014	0.310039	0.000046	0.023508	0.000389	0.029993	0.339877	1.125849	2004-03-10 18:00:00	2004-04-27 23:00:00	1158	27.198789	27.216369	1.736979	1.000646	0.063862	15.668791	0.023508	27.216369	0.001501	0.03873	1.280324	2004-04-28	2004-05-01	73	2.159501	6.272988	8.432482	2.904833	3.90483	0.743908	0.029993	6.272988	0.029993	0.339873	1.125817

Improvement Model

Univariate: ARDL, SARIMAX, SVM
- Target(5): 'PT08.S1(CO)', 'PT08.S2(NMHC)', 'PT08.S3(NOx)', 'PT08.S4(NO2)', 'PT08.S5(O3)'
- h-step forecast evaluation
- [Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
- [Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73

			start	end	scenario	total	sst	ssr	sse	ssr/sst	sse/sst	ssr/sse	mst	msr	mse	rmse	mape
note	domain_kind	model
PT08.S1(CO)	test	ARDL	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.363559e+06	1.592328e+06	5.298400e+05	1.167773	0.388571	3.005300	18938.320225	8.380674e+04	4157.404298	85.194381	2.525607
		LinearSVR	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.363559e+06	1.277322e+06	7.226992e+04	0.936756	0.053001	17.674321	18938.320225	4.561863e+04	1584.218037	31.464248	0.780669
		SARIMAX	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.363559e+06	1.817311e+06	3.533621e+05	1.332770	0.259147	5.142915	18938.320225	1.397931e+05	3133.572945	69.574250	1.588113
	train	ARDL	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.732967e+07	3.285384e+07	4.450862e+06	0.880100	0.119231	7.381455	32264.189139	1.729150e+06	3914.566782	62.050198	1.301650
		LinearSVR	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.732967e+07	3.588555e+07	1.461420e+06	0.961315	0.039149	24.555270	32264.189139	1.281627e+06	1292.377119	35.524926	0.811643
		SARIMAX	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.732967e+07	3.815579e+07	1.351412e+06	1.022130	0.036202	28.234027	32264.189139	2.935061e+06	1180.271172	34.161705	0.759937
PT08.S2(NMHC)	test	ARDL	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.367597e+06	1.628822e+06	7.083755e+04	1.191011	0.051797	22.993770	18994.399669	8.572749e+04	1305.730560	31.150880	0.402409
		LinearSVR	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.367597e+06	1.609306e+06	4.022362e+04	1.176740	0.029412	40.008983	18994.399669	5.747522e+04	815.637473	23.473569	0.284144
		SARIMAX	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.367597e+06	1.500905e+06	5.445007e+04	1.097476	0.039814	27.564787	18994.399669	1.154542e+05	730.860237	27.311012	0.347112
	train	ARDL	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.947260e+07	3.815931e+07	1.214012e+06	0.966729	0.030756	31.432401	34116.338096	2.008385e+06	1067.732492	32.406531	0.537517
		LinearSVR	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.947260e+07	4.073622e+07	7.153512e+05	1.032013	0.018123	56.945763	34116.338096	1.454865e+06	632.537290	24.854521	0.431385
		SARIMAX	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.947260e+07	3.804603e+07	6.851516e+05	0.963859	0.017358	55.529360	34116.338096	2.926618e+06	598.384755	24.324228	0.363650
PT08.S3(NOx)	test	ARDL	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	6.140767e+05	9.816835e+05	8.655285e+05	1.598633	1.409479	1.134201	8528.843129	5.166755e+04	15413.107054	108.887808	0.570109
		LinearSVR	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	6.140767e+05	8.963472e+05	2.064890e+05	1.459666	0.336259	4.340896	8528.843129	3.201240e+04	4351.676994	53.184736	0.270153
		SARIMAX	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	6.140767e+05	8.446576e+05	4.360814e+05	1.375492	0.710142	1.936927	8528.843129	6.033269e+04	7267.127889	77.289830	0.342547
	train	ARDL	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	4.289261e+07	3.592588e+07	6.731408e+06	0.837577	0.156936	5.337053	37072.268300	1.890836e+06	5920.323439	76.308696	3.104840
		LinearSVR	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	4.289261e+07	4.306446e+07	4.273258e+06	1.004006	0.099627	10.077665	37072.268300	1.538016e+06	3779.092038	60.747059	2.002940
		SARIMAX	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	4.289261e+07	3.842578e+07	4.068667e+06	0.895860	0.094857	9.444315	37072.268300	2.744698e+06	3556.378714	59.275035	2.714925
PT08.S4(NO2)	test	ARDL	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	2.487513e+06	2.800260e+06	1.393040e+05	1.125727	0.056001	20.101799	34548.793047	1.473821e+05	1366.575486	43.683789	0.370328
		LinearSVR	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	2.487513e+06	2.335696e+06	5.726143e+04	0.938969	0.023020	40.790050	34548.793047	8.341773e+04	1111.148154	28.007197	0.257784
		SARIMAX	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	2.487513e+06	2.666173e+06	7.631002e+04	1.071823	0.030677	34.938696	34548.793047	2.050902e+05	1157.136276	32.331762	0.448569
	train	ARDL	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	5.377491e+07	5.202426e+07	1.626461e+06	0.967445	0.030246	31.986165	46477.882878	2.738119e+06	1430.484935	37.509645	5.159292
		LinearSVR	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	5.377491e+07	4.907647e+07	1.322227e+06	0.912628	0.024588	37.116538	46477.882878	1.752731e+06	1167.876051	33.790815	2.236627
		SARIMAX	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	5.377491e+07	5.367240e+07	1.037607e+06	0.998094	0.019295	51.727075	46477.882878	4.128646e+06	906.165326	29.933828	2.179873
PT08.S5(O3)	test	ARDL	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	3.547900e+06	2.988311e+06	7.365706e+05	0.842276	0.207607	4.057060	49276.386463	1.572795e+05	13470.632327	100.449033	0.822711
		LinearSVR	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	3.547900e+06	3.445754e+06	4.627351e+05	0.971209	0.130425	7.446494	49276.386463	1.230626e+05	10274.026451	79.616810	0.858060
		SARIMAX	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	3.547900e+06	3.258993e+06	1.162249e+06	0.918570	0.327588	2.804040	49276.386463	2.506918e+05	14616.319061	126.179311	1.053004
	train	ARDL	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	1.117786e+08	1.034142e+08	8.219973e+06	0.925170	0.073538	12.580850	96610.733585	5.442855e+06	7229.528078	84.324988	1.084783
		LinearSVR	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	1.117786e+08	1.122560e+08	4.474445e+06	1.004271	0.040030	25.088249	96610.733585	4.009142e+06	3959.466735	62.160615	0.726864
		SARIMAX	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	1.117786e+08	1.041239e+08	4.617267e+06	0.931519	0.041307	22.550975	96610.733585	8.009529e+06	4031.971021	63.144891	0.672294

Multivariate: VARMAX[Reduced, Structural-Orthogonal Residual]

			datetime	start	end	scenario	total	sst	ssr	sse	ssr/sst	sse/sst	ssr/sse	mst	msr	mse	rmse	mape
note	domain_kind	model
PT08.S1(CO)	Train	VAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.732967e+07	3.440836e+07	6.167148e+06	0.921743	0.165208	5.579298	32264.189139	1.810966e+06	5414.502498	72.977318	1.625518
	Train	SVAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.732967e+07	3.038897e+07	3.844580e+06	0.814070	0.102990	7.904366	32264.189139	1.599419e+06	3374.552238	57.619593	1.292810
	Test	VAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.363559e+06	8.841824e+05	5.856959e+05	0.648437	0.429535	1.509627	18938.320225	4.653591e+04	9966.437971	89.572493	2.808808
	Test	SVAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.363559e+06	1.277609e+06	3.308650e+05	0.936966	0.242648	3.861420	18938.320225	6.724256e+04	4379.542870	67.323083	6.351021
PT08.S2(NMHC)	Train	VAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.947260e+07	3.688051e+07	4.972394e+06	0.934332	0.125971	7.417053	34116.338096	1.941080e+06	4365.500487	65.528239	1.709778
	Train	SVAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	3.947260e+07	3.553729e+07	2.001193e+06	0.900303	0.050698	17.758050	34116.338096	1.870383e+06	1756.407807	41.570976	0.991264
	Test	VAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.367597e+06	8.860699e+05	5.025864e+05	0.647903	0.367496	1.763020	18994.399669	4.663526e+04	9297.071156	82.974368	0.803243
	Test	SVAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	1.367597e+06	1.388727e+06	1.974476e+05	1.015451	0.144376	7.033398	18994.399669	7.309092e+04	3360.463086	52.007321	0.631011
PT08.S3(NOx)	Train	VAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	4.289261e+07	4.000426e+07	5.003658e+06	0.932661	0.116655	7.995002	37072.268300	2.105487e+06	4393.006428	65.733923	1.940422
	Train	SVAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	4.289261e+07	3.838154e+07	4.556670e+06	0.894829	0.106234	8.423156	37072.268300	2.020081e+06	4000.048144	62.729162	1.937093
	Test	VAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	6.140767e+05	1.790916e+06	1.491800e+06	2.916437	2.429339	1.200507	8528.843129	9.425875e+04	27227.273700	142.953215	0.726407
	Test	SVAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	6.140767e+05	2.087912e+06	1.445818e+06	3.400084	2.354459	1.444104	8528.843129	1.098901e+05	26371.402302	140.732827	0.592418
PT08.S4(NO2)	Train	VAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	5.377491e+07	4.580911e+07	1.225976e+07	0.851868	0.227983	3.736542	46477.882878	2.411006e+06	10763.456546	102.893212	2.882381
	Train	SVAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	5.377491e+07	4.531533e+07	4.802234e+06	0.842685	0.089302	9.436304	46477.882878	2.385018e+06	4212.798105	64.397256	10.319381
	Test	VAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	2.487513e+06	1.205716e+06	1.228865e+06	0.484708	0.494013	0.981163	34548.793047	6.345875e+04	22407.270330	129.745001	0.739179
	Test	SVAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	2.487513e+06	2.151442e+06	4.136605e+05	0.864897	0.166295	5.200986	34548.793047	1.132338e+05	6242.583281	75.276700	0.578552
PT08.S5(O3)	Train	VAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	1.117786e+08	1.018719e+08	9.551881e+06	0.911372	0.085454	10.665114	96610.733585	5.361679e+06	8386.052792	90.821816	1.157383
	Train	SVAR	2023-08-28 15:06:01	2004-03-10 18:00:00	2004-04-27 23:00:00	Time Series Analysis	1158	1.117786e+08	1.158184e+08	9.305864e+06	1.036141	0.083253	12.445746	96610.733585	6.095706e+06	8170.008120	89.644588	1.336284
	Test	VAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	3.547900e+06	2.329879e+06	1.449389e+06	0.656693	0.408520	1.607490	49276.386463	1.226252e+05	23623.928166	140.906524	1.434259
	Test	SVAR	2023-08-28 15:06:01	2004-04-28 00:00:00	2004-05-01 00:00:00	Time Series Analysis	73	3.547900e+06	7.067373e+06	3.579318e+06	1.991988	1.008855	1.974503	49276.386463	3.719670e+05	47682.765355	221.431144	2.086808

Time Series Model Design

Overall Model Specification

Baseline model

Naive forecast model

endogenous variables: 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5', 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)', 'T', 'RH', 'AH'
[Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
[Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73

ETS model: Addictive Dampping Trend

endogenous variables: 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5', 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)', 'T', 'RH', 'AH'
[Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
[Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73

Improvement model

Short-term forecast model

Univariate approach
- ARDL: Autoregressive Distributed Lag Model
  - endogenous variables[-2 lag]: 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5'
  - exogenous variables[-2 lag]: 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)', 'T', 'RH', 'AH'
  - bias: constant
  - [Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
  - [Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73
  - (note) Stationary Constraint[False], Integration Structure[False], Error Correction[False], Distributed Lag[True]
- SARIMAX: Autoregressive Moving Average Model
  - endogenous variables[-1,-2 lag]: 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5'
  - exogenous variables: 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)', 'T', 'RH', 'AH'
  - bias: constant
  - constant volatility: -1, -2 lag
  - [Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
  - [Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73
  - (note) Stationary Constraint[True], Integration Structure[True], Error Correction[False], Distributed Lag[False]
- SVM: Support Vector Machine
  - endogenous variables[-2lag]: 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5'
  - fixed exogenous variables[-2lag]: 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)', 'T', 'RH', 'AH'
  - bias: constant
  - [Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
  - [Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73
  - (note) Stationary Constraint[False], Integration Structure[True], Error Correction[True], Distributed Lag[True]
Multivariate approach
- VARMAX: Vector Autoregressive Moving Average Model
  - endogenous variables[-2lag]: 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5'
  - exogenous variables: 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)', 'T', 'RH', 'AH'
  - bias: constant
  - [Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
  - [Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73
  - (note) Stationary Constraint[True], Integration Structure[False], Constraint Error Correction[False], Distributed Lag[False]
- VECM: Vector Error Correction Model
  - endogenous variables[-2lag]: 'PT08.S1', 'PT08.S2', 'PT08.S3', 'PT08.S4', 'PT08.S5'
  - exogenous variables: 'T', 'RH', 'AH'
  - coint exogenous variables[-lag]: 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)'
  - bias: constant
  - cointegration rank: 4
  - [Train Period]: 2004-03-10 18:00:00 ~ 2004-04-27 23:00:00, 1158
  - [Test Period]: 2004-04-28 00:00:00 ~ 2004-05-01 00:00:00, 73
  - (note) Stationary Constraint[True], Integration Structure[True], Constraint Error Correction[True], Distributed Lag[False]

Base Preprocessing for Forecasting Pollutants Variables

Statistical characteristics preprocessing: mean-centering[False], variance-centering[False]
Time Series characteristics preprocessing: lag shift[True], trend difference[True], seasonal difference[False]

$${\displaystyle Y_{i,t} = \underbrace{{\color{Red}{Y_{i,t}^{\text{stochastic process}}}}}_{\text{Modeling}} + Y_{i,t}^{\text{deterministic seasonal(24) process}} \\ }$$ $${\displaystyle y_{i,t} \equiv Y_{i,t}^{\text{stochastic process}} }$$ $${\displaystyle \begin{split}\begin{align} \text{mean centering}: \quad & y_{i,t} \rightarrow y_{i,t} - \operatorname{E} [y_{i,t}] \\ \text{variance centering}: \quad & y_{i,t} \rightarrow \frac{y_{i,t} - \operatorname{E} [y_{i,t}](1 - \operatorname{Var} [y_{i,t}] )}{\operatorname{Var}[y_{i,t}]} \\ \text{lag shift}: \quad & y_{i,t} \rightarrow y_{i,t-j} \\ \text{trend difference}: \quad & y_{i,t} \rightarrow \Delta y_{i,t}\\ \text{seasonal difference}: \quad & y_{i,t} \rightarrow y_{i,t-m \cdot j}, \quad \text{for seasonal period with }m \text{ } \\ \end{align}\end{split} }$$

Multivariate Time Series Characteristic Analysis

[Note] Dynamic Facot Analysis (DFA), Principal Component Analysis (PCA), and Cointegration Analysis were conducted on deseasonalized time series data.

Dynamic Factor Analysis

Dynamic Factor Analysis (DFA) uncovers common factors that can explain multiple given time series data collectively. This method aims to go beyond individual approachs for each time series data and seeks integrated insights by understanding the interrelationships among them. Also, DFA involves reducing the dimensions of the given multidimensional data while explaining the variablility in the data by extracting significant dynamic factors. These factors can reveal shared structures or relationships among the given time series data. Consequently, it helps to identify patterns, similarities, and correlations among the data, providing a comprehensive overview.

Dynamic factor analysis can be seen as an extended version of Principal Component Analysis (PCA) applied to time series data. While PCA primarily focuses on extracting principal components that explain the variability in the data, dynamic factor analysis emphasizes extracting factors while considering the temporal structure of the time series data. This approach allows us to understand interactions and dynamic relationships among multiple time series data, shedding light on how these data sets mutually influence each other.

	coef	std err	z	P>\|z\|	[0.025	0.975]

L1.f1.f1	0.0489	0.027	1.779	0.075	-0.005	0.103
L2.f1.f1	-0.2070	0.031	-6.708	0.000	-0.268	-0.147

$${\displaystyle \begin{split}\begin{align} Y_{i,t} & = Y_{i,t}^{\text{stochastic process}} + Y_{i,t}^{\text{deterministic seasonal(24) process}} \\ y_{i,t}^{\text{stochastic process}} &= \frac{\overline{Y}_{i,t}^{\text{stochastic process}} - Y_{i,t}^{\text{stochastic process}}}{\sigma_{Y_{i,t}^{\text{stochastic process}}}} \\ y_{i,t} & \equiv \Delta^{1} y_{i,t}^{\text{stochastic process}} \\ y_{i,t} & = \lambda_i f_t + u_{i,t} \\ u_{i,t} & = c_{i,1} u_{1,t-1} + c_{i,2} u_{i,t-2} + \varepsilon_{i,t} \qquad & \varepsilon_{i,t} \sim N(0, \sigma_i^2) \\ f_t & = 0.0489 f_{t-1} -0.2070 f_{t-2} + \eta_t \qquad & \eta_t \sim N(0, I)\\ \end{align}\end{split} }$$

Comparison between original trend and unique loadings

Result for factor analysis

		First Factor Common Loadings							Unique Loadings Variance							Lag1							Lag2
		coef	std err	z	P>\|z\|	[0.025	0.975]		coef	std err	z	P>\|z\|	[0.025	0.975]		coef	std err	z	P>\|z\|	[0.025	0.975]		coef	std err	z	P>\|z\|	[0.025	0.975]
CO(GT)	loading.f1.CO(GT)	-0.5623	0.018	-30.888	0.000	-0.598	-0.527	sigma2.CO(GT)	0.1611	0.007	23.919	0.000	0.148	0.174	L1.e(CO(GT)).e(CO(GT))	-0.1209	0.028	-4.330	0.000	-0.176	-0.066	L2.e(CO(GT)).e(CO(GT))	-0.2414	0.032	-7.539	0.000	-0.304	-0.179
PT08.S1(CO)	loading.f1.PT08.S1(CO)	-0.5346	0.012	-44.319	0.000	-0.558	-0.511	sigma2.PT08.S1(CO)	0.0341	0.001	23.153	0.000	0.031	0.037	L1.e(PT08.S1(CO)).e(PT08.S1(CO))	-0.2784	0.029	-9.497	0.000	-0.336	-0.221	L2.e(PT08.S1(CO)).e(PT08.S1(CO))	-0.1702	0.033	-5.159	0.000	-0.235	-0.106
NMHC(GT)	loading.f1.NMHC(GT)	-0.4683	0.018	-25.642	0.000	-0.504	-0.432	sigma2.NMHC(GT)	0.2610	0.008	31.868	0.000	0.245	0.277	L1.e(NMHC(GT)).e(NMHC(GT))	-0.0974	0.025	-3.916	0.000	-0.146	-0.049	L2.e(NMHC(GT)).e(NMHC(GT))	-0.2291	0.029	-7.808	0.000	-0.287	-0.172
C6H6(GT)	loading.f1.C6H6(GT)	-0.6151	0.015	-41.809	0.000	-0.644	-0.586	sigma2.C6H6(GT)	0.0219	0.001	19.103	0.000	0.020	0.024	L1.e(C6H6(GT)).e(C6H6(GT))	-0.1276	0.034	-3.755	0.000	-0.194	-0.061	L2.e(C6H6(GT)).e(C6H6(GT))	-0.1920	0.045	-4.289	0.000	-0.280	-0.104
PT08.S2(NMHC)	loading.f1.PT08.S2(NMHC)	-0.5711	0.012	-48.124	0.000	-0.594	-0.548	sigma2.PT08.S2(NMHC)	0.0072	0.001	9.625	0.000	0.006	0.009	L1.e(PT08.S2(NMHC)).e(PT08.S2(NMHC))	0.3806	0.067	5.675	0.000	0.249	0.512	L2.e(PT08.S2(NMHC)).e(PT08.S2(NMHC))	-0.3231	0.055	-5.823	0.000	-0.432	-0.214
NOx(GT)	loading.f1.NOx(GT)	-0.4926	0.022	-22.761	0.000	-0.535	-0.450	sigma2.NOx(GT)	0.1989	0.009	22.596	0.000	0.182	0.216	L1.e(NOx(GT)).e(NOx(GT))	-0.1743	0.030	-5.816	0.000	-0.233	-0.116	L2.e(NOx(GT)).e(NOx(GT))	-0.2059	0.032	-6.467	0.000	-0.268	-0.143
PT08.S3(NOx)	loading.f1.PT08.S3(NOx)	0.3863	0.020	19.610	0.000	0.348	0.425	sigma2.PT08.S3(NOx)	0.0846	0.003	29.112	0.000	0.079	0.090	L1.e(PT08.S3(NOx)).e(PT08.S3(NOx))	0.1887	0.024	7.765	0.000	0.141	0.236	L2.e(PT08.S3(NOx)).e(PT08.S3(NOx))	-0.2037	0.027	-7.586	0.000	-0.256	-0.151
NO2(GT)	loading.f1.NO2(GT)	-0.3610	0.021	-16.892	0.000	-0.403	-0.319	sigma2.NO2(GT)	0.2572	0.011	23.704	0.000	0.236	0.278	L1.e(NO2(GT)).e(NO2(GT))	-0.1683	0.025	-6.684	0.000	-0.218	-0.119	L2.e(NO2(GT)).e(NO2(GT))	-0.2548	0.028	-9.033	0.000	-0.310	-0.200
PT08.S4(NO2)	loading.f1.PT08.S4(NO2)	-0.5643	0.012	-45.571	0.000	-0.589	-0.540	sigma2.PT08.S4(NO2)	0.0219	0.000	59.972	0.000	0.021	0.023	L1.e(PT08.S4(NO2)).e(PT08.S4(NO2))	-0.5146	0.013	-39.464	0.000	-0.540	-0.489	L2.e(PT08.S4(NO2)).e(PT08.S4(NO2))	-0.2518	0.024	-10.355	0.000	-0.299	-0.204
PT08.S5(O3)	loading.f1.PT08.S5(O3)	-0.4193	0.010	-40.343	0.000	-0.440	-0.399	sigma2.PT08.S5(O3)	0.0413	0.001	28.347	0.000	0.038	0.044	L1.e(PT08.S5(O3)).e(PT08.S5(O3))	0.0484	0.027	1.781	0.075	-0.005	0.102	L2.e(PT08.S5(O3)).e(PT08.S5(O3))	-0.1730	0.032	-5.397	0.000	-0.236	-0.110
T	loading.f1.T	0.0041	0.019	0.212	0.832	-0.033	0.042	sigma2.T	0.0731	0.004	20.496	0.000	0.066	0.080	L1.e(T).e(T)	0.2739	0.034	8.042	0.000	0.207	0.341	L2.e(T).e(T)	-0.0180	0.038	-0.472	0.637	-0.093	0.057
RH	loading.f1.RH	-0.0403	0.032	-1.257	0.209	-0.103	0.022	sigma2.RH	0.1186	0.005	24.486	0.000	0.109	0.128	L1.e(RH).e(RH)	0.2269	0.029	7.957	0.000	0.171	0.283	L2.e(RH).e(RH)	-0.0631	0.034	-1.876	0.061	-0.129	0.003
AH	loading.f1.AH	-0.0488	0.014	-3.496	0.000	-0.076	-0.021	sigma2.AH	0.0505	0.001	33.690	0.000	0.048	0.053	L1.e(AH).e(AH)	0.1954	0.021	9.206	0.000	0.154	0.237	L2.e(AH).e(AH)	-0.1380	0.027	-5.180	0.000	-0.190	-0.086

Diagnostics for residual

There exists a limitation of non-conformity to normality for the residuals. This stems from training with only one extracted factor. It is anticipated that an enhancement could be achieved by increasing the number of factors.

	Autocorrelation			Heteroskedasticity			Normality
	Ljung-Box (L1) (Q)	Prob(Q)	Reject	Heteroskedasticity (H)	Prob(H) (two-sided)	Reject	Jarque-Bera (JB)	Prob(JB)	Skew	Kurtosis	Reject
Residual
CO(GT)	0.62	0.43	False	0.64	0.00	True	762.43	0.0	0.41	6.77	False
PT08.S1(CO)	0.00	0.99	False	1.96	0.00	True	385.30	0.0	0.25	5.70	False
NMHC(GT)	2.44	0.12	False	1.27	0.02	True	979.78	0.0	0.23	7.35	False
C6H6(GT)	0.45	0.50	False	1.29	0.01	True	1584.67	0.0	0.05	8.56	False
PT08.S2(NMHC)	5.72	0.02	True	0.91	0.34	False	36.53	0.0	-0.08	3.83	False
NOx(GT)	0.81	0.37	False	1.19	0.08	False	519.95	0.0	-0.07	6.18	False
PT08.S3(NOx)	2.13	0.14	False	0.74	0.00	True	502.91	0.0	0.10	6.13	False
NO2(GT)	2.59	0.11	False	0.77	0.01	True	59.82	0.0	0.08	4.07	False
PT08.S4(NO2)	0.05	0.83	False	1.12	0.27	False	198431.95	0.0	-2.34	65.05	False
PT08.S5(O3)	0.46	0.50	False	0.85	0.10	False	356.53	0.0	0.46	5.48	False
T	0.00	0.99	False	1.21	0.05	False	708.67	0.0	-0.27	6.68	False
RH	0.00	1.00	False	1.03	0.74	False	3498.46	0.0	0.56	11.19	False
AH	0.03	0.87	False	1.31	0.01	True	2153.34	0.0	0.71	9.32	False

Principal Component Analysis

Principal Component Analysis (PCA) is a widely used statistical technique for analyzing and reducing the dimensions of multivariate data. It aims to capture the most important information or patterns in the data while discarding or minimizing the less important information. PCA achieves this by transforming the original variables into a new set of uncorrelated variables called principal components.

Cointegration Analysis

Bivariate cointegration Analysis

cointegration for deseasonalized time series

[PT08.S1(CO)]: PT08.S2(NMHC), NOx(GT), NO2(GT), CO(GT)
[PT08.S2(NMHC)]: PT08.S1(CO), PT08.S4(NO2), PT08.S5(O3), CO(GT), C6H6(GT), T, AH
[PT08.S3(NOx)]: PT08.S4(NO2), PT08.S5(O3), CO(GT), NMHC(GT), C6H6(GT), NOx(GT), NO2(GT), T, RH, AH
[PT08.S4(NO2)]: PT08.S2(NMHC), PT08.S3(NOx), C6H6(GT)
[PT08.S5(O3)]: PT08.S2(NMHC), PT08.S3(NOx), CO(GT), C6H6(GT), NOx(GT), NO2(GT), AH

	Cointegration							RV1ResidualStationary								RV2ResidualStationary								Cointegration
	rv1	rv2	t-statistic	p-val	crit1	crit5	crit10	t-statistic	p-val	used_lag	nobs	crit1	crit5	crit10	icbest	t-statistic	p-val	used_lag	nobs	crit1	crit5	crit10	icbest	Determination
0	CO(GT)	PT08.S1(CO)	-7.295834	1.667493e-09	-3.905366	-3.341102	-3.0479	-7.294736	1.387455e-10	8	1222	-3.435713	-2.863908	-2.568031	1046.851611	-3.519355	7.503711e-03	23	1207	-3.435779	-2.863938	-2.568046	13444.258432	True
1	CO(GT)	PT08.S2(NMHC)	-3.747276	1.591290e-02	-3.905366	-3.341102	-3.0479	-3.745636	3.515157e-03	23	1207	-3.435779	-2.863938	-2.568046	1030.167743	-3.264312	1.655105e-02	23	1207	-3.435779	-2.863938	-2.568046	13596.564121	True
2	CO(GT)	NOx(GT)	-4.429011	1.598218e-03	-3.905366	-3.341102	-3.0479	-4.425954	2.669638e-04	23	1207	-3.435779	-2.863938	-2.568046	328.344393	-4.433306	2.590360e-04	23	1207	-3.435779	-2.863938	-2.568046	10181.944235	True
3	CO(GT)	PT08.S3(NOx)	-3.987745	7.475540e-03	-3.905366	-3.341102	-3.0479	-3.990248	1.462444e-03	23	1207	-3.435779	-2.863938	-2.568046	1695.232821	-3.926294	1.849637e-03	22	1208	-3.435775	-2.863936	-2.568045	14060.499323	True
4	CO(GT)	NO2(GT)	-4.342215	2.198459e-03	-3.905366	-3.341102	-3.0479	-4.332872	3.894570e-04	23	1207	-3.435779	-2.863938	-2.568046	1484.290900	-4.046021	1.187804e-03	23	1207	-3.435779	-2.863938	-2.568046	8915.923324	True
5	CO(GT)	PT08.S5(O3)	-4.837217	3.242708e-04	-3.905366	-3.341102	-3.0479	-4.836122	4.636230e-05	23	1207	-3.435779	-2.863938	-2.568046	1309.219236	-3.808615	2.820391e-03	22	1208	-3.435775	-2.863936	-2.568045	14895.258012	True
6	CO(GT)	T	-3.451260	3.696768e-02	-3.905366	-3.341102	-3.0479	-3.448194	9.421624e-03	23	1207	-3.435779	-2.863938	-2.568046	2177.922142	-3.369108	1.205815e-02	23	1207	-3.435779	-2.863938	-2.568046	3541.283688	True
7	CO(GT)	RH	-3.410705	4.117532e-02	-3.905366	-3.341102	-3.0479	-3.408693	1.066606e-02	23	1207	-3.435779	-2.863938	-2.568046	2173.113060	-7.000788	7.331272e-10	7	1223	-3.435708	-2.863906	-2.568030	6784.747928	True
8	CO(GT)	AH	-3.950840	8.428314e-03	-3.905366	-3.341102	-3.0479	-3.950521	1.692950e-03	23	1207	-3.435779	-2.863938	-2.568046	2157.102440	-3.595769	5.842435e-03	9	1221	-3.435717	-2.863910	-2.568032	-3847.679236	True
9	PT08.S1(CO)	PT08.S2(NMHC)	-3.662927	2.043521e-02	-3.905366	-3.341102	-3.0479	-3.669221	4.567518e-03	18	1212	-3.435757	-2.863928	-2.568041	12173.907550	-5.201615	8.725575e-06	8	1222	-3.435713	-2.863908	-2.568031	12354.828445	True
10	PT08.S1(CO)	NOx(GT)	-3.399306	4.242766e-02	-3.905366	-3.341102	-3.0479	-3.398576	1.100751e-02	23	1207	-3.435779	-2.863938	-2.568046	13616.376740	-6.889800	1.364878e-09	9	1221	-3.435717	-2.863910	-2.568032	11026.449562	True
11	PT08.S1(CO)	NO2(GT)	-3.454223	3.667491e-02	-3.905366	-3.341102	-3.0479	-3.448264	9.419542e-03	23	1207	-3.435779	-2.863938	-2.568046	14049.379278	-7.348524	1.020419e-10	9	1221	-3.435717	-2.863910	-2.568032	8991.692280	True
12	NMHC(GT)	PT08.S3(NOx)	-14.390939	7.974083e-26	-3.905366	-3.341102	-3.0479	-14.385185	9.014536e-27	2	1228	-3.435686	-2.863896	-2.568025	14059.837908	-8.318992	3.615332e-13	5	1225	-3.435699	-2.863902	-2.568028	14304.029751	True
13	NMHC(GT)	T	-3.925943	9.131333e-03	-3.905366	-3.341102	-3.0479	-3.926583	1.847689e-03	23	1207	-3.435779	-2.863938	-2.568046	14329.985341	-3.137825	2.387766e-02	22	1208	-3.435775	-2.863936	-2.568045	3803.168754	True
14	NMHC(GT)	RH	-3.733993	1.656077e-02	-3.905366	-3.341102	-3.0479	-3.737017	3.621601e-03	23	1207	-3.435779	-2.863938	-2.568046	14335.610189	-7.995953	2.404064e-12	1	1229	-3.435682	-2.863895	-2.568024	6769.329755	True
15	NMHC(GT)	AH	-4.627549	7.500186e-04	-3.905366	-3.341102	-3.0479	-4.631431	1.129930e-04	23	1207	-3.435779	-2.863938	-2.568046	14327.370198	-4.937199	2.950334e-05	2	1228	-3.435686	-2.863896	-2.568025	-3754.712726	True
16	C6H6(GT)	PT08.S2(NMHC)	-4.494821	1.248891e-03	-3.905366	-3.341102	-3.0479	-4.492322	2.030179e-04	23	1207	-3.435779	-2.863938	-2.568046	2991.887523	-4.242326	5.582399e-04	23	1207	-3.435779	-2.863938	-2.568046	11458.551574	True
17	C6H6(GT)	PT08.S3(NOx)	-3.341117	4.932446e-02	-3.905366	-3.341102	-3.0479	-3.345402	1.296702e-02	23	1207	-3.435779	-2.863938	-2.568046	5465.016999	-3.746829	3.500654e-03	22	1208	-3.435775	-2.863936	-2.568045	13711.805397	True
18	C6H6(GT)	PT08.S4(NO2)	-3.390534	4.341279e-02	-3.905366	-3.341102	-3.0479	-3.385736	1.145485e-02	19	1211	-3.435761	-2.863930	-2.568042	3490.381272	-6.436550	1.647404e-08	2	1228	-3.435686	-2.863896	-2.568025	12228.558737	True
19	C6H6(GT)	PT08.S5(O3)	-3.980070	7.665274e-03	-3.905366	-3.341102	-3.0479	-3.980435	1.516499e-03	23	1207	-3.435779	-2.863938	-2.568046	4814.847207	-3.429492	9.993647e-03	23	1207	-3.435779	-2.863938	-2.568046	14281.517761	True
20	C6H6(GT)	T	-3.420487	4.012542e-02	-3.905366	-3.341102	-3.0479	-3.417969	1.036134e-02	23	1207	-3.435779	-2.863938	-2.568046	6231.506142	-3.466463	8.891342e-03	23	1207	-3.435779	-2.863938	-2.568046	3884.010504	True
21	C6H6(GT)	AH	-3.403249	4.199088e-02	-3.905366	-3.341102	-3.0479	-3.403418	1.084289e-02	23	1207	-3.435779	-2.863938	-2.568046	6218.091602	-3.867152	2.290341e-03	7	1223	-3.435708	-2.863906	-2.568030	-4095.951931	True
22	PT08.S2(NMHC)	PT08.S4(NO2)	-3.646655	2.142610e-02	-3.905366	-3.341102	-3.0479	-3.643185	4.987105e-03	19	1211	-3.435761	-2.863930	-2.568042	11955.661649	-4.772569	6.135271e-05	9	1221	-3.435717	-2.863910	-2.568032	12424.244492	True
23	PT08.S2(NMHC)	PT08.S5(O3)	-4.001632	7.142924e-03	-3.905366	-3.341102	-3.0479	-4.002383	1.398082e-03	23	1207	-3.435779	-2.863938	-2.568046	12796.766940	-3.628374	5.241185e-03	22	1208	-3.435775	-2.863936	-2.568045	13798.462833	True
24	PT08.S2(NMHC)	T	-3.409912	4.126141e-02	-3.905366	-3.341102	-3.0479	-3.407089	1.071955e-02	22	1208	-3.435775	-2.863936	-2.568045	14601.280067	-3.479724	8.523358e-03	23	1207	-3.435779	-2.863938	-2.568046	3812.854867	True
25	PT08.S2(NMHC)	AH	-3.497560	3.261231e-02	-3.905366	-3.341102	-3.0479	-3.497576	8.049566e-03	22	1208	-3.435775	-2.863936	-2.568045	14561.669841	-3.993126	1.446935e-03	7	1223	-3.435708	-2.863906	-2.568030	-4102.051060	True
26	NOx(GT)	PT08.S3(NOx)	-3.972449	7.857974e-03	-3.905366	-3.341102	-3.0479	-3.976581	1.538230e-03	23	1207	-3.435779	-2.863938	-2.568046	11507.299261	-3.929957	1.825111e-03	21	1209	-3.435770	-2.863934	-2.568044	13994.311970	True
27	NOx(GT)	NO2(GT)	-14.440195	6.635408e-26	-3.905366	-3.341102	-3.0479	-14.434119	7.545213e-27	2	1228	-3.435686	-2.863896	-2.568025	10839.311326	-12.762040	8.104430e-24	2	1228	-3.435686	-2.863896	-2.568025	8397.529904	True
28	NOx(GT)	PT08.S5(O3)	-4.818442	3.501191e-04	-3.905366	-3.341102	-3.0479	-4.814731	5.096475e-05	23	1207	-3.435779	-2.863938	-2.568046	11137.117050	-3.759384	3.351300e-03	23	1207	-3.435779	-2.863938	-2.568046	14863.349608	True
29	NOx(GT)	T	-3.468602	3.528209e-02	-3.905366	-3.341102	-3.0479	-3.466439	8.892032e-03	23	1207	-3.435779	-2.863938	-2.568046	12001.623297	-3.370376	1.201117e-02	23	1207	-3.435779	-2.863938	-2.568046	3420.532654	True
30	NOx(GT)	RH	-3.484945	3.375349e-02	-3.905366	-3.341102	-3.0479	-3.483434	8.422877e-03	23	1207	-3.435779	-2.863938	-2.568046	11982.667303	-8.016872	2.127254e-12	1	1229	-3.435682	-2.863895	-2.568024	6772.603716	True
31	NOx(GT)	AH	-3.789475	1.400009e-02	-3.905366	-3.341102	-3.0479	-3.788043	3.032045e-03	23	1207	-3.435779	-2.863938	-2.568046	11975.148088	-4.406412	2.891716e-04	4	1226	-3.435695	-2.863900	-2.568027	-4031.305638	True
32	PT08.S3(NOx)	NO2(GT)	-3.454900	3.660838e-02	-3.905366	-3.341102	-3.0479	-3.465596	8.915905e-03	22	1208	-3.435775	-2.863936	-2.568045	13975.871802	-3.564677	6.473374e-03	22	1208	-3.435775	-2.863936	-2.568045	9046.197972	True
33	PT08.S3(NOx)	PT08.S4(NO2)	-4.226399	3.325655e-03	-3.905366	-3.341102	-3.0479	-4.252339	5.366432e-04	22	1208	-3.435775	-2.863936	-2.568045	13506.666744	-3.021526	3.293246e-02	23	1207	-3.435779	-2.863938	-2.568046	14079.554752	True
34	PT08.S3(NOx)	PT08.S5(O3)	-3.491750	3.313379e-02	-3.905366	-3.341102	-3.0479	-3.517830	7.540815e-03	22	1208	-3.435775	-2.863936	-2.568045	13050.543689	-2.938197	4.108311e-02	21	1209	-3.435770	-2.863934	-2.568044	14162.528573	True
35	PT08.S3(NOx)	T	-3.781301	1.435389e-02	-3.905366	-3.341102	-3.0479	-3.783663	3.078961e-03	23	1207	-3.435779	-2.863938	-2.568046	14370.577284	-3.681439	4.381935e-03	17	1213	-3.435752	-2.863926	-2.568040	3714.912190	True
36	PT08.S3(NOx)	RH	-3.620887	2.308052e-02	-3.905366	-3.341102	-3.0479	-3.628257	5.243237e-03	23	1207	-3.435779	-2.863938	-2.568046	14253.920601	-6.774255	2.594867e-09	7	1223	-3.435708	-2.863906	-2.568030	6701.073556	True
37	PT08.S3(NOx)	AH	-4.613064	7.935735e-04	-3.905366	-3.341102	-3.0479	-4.622658	1.173022e-04	23	1207	-3.435779	-2.863938	-2.568046	14193.389584	-4.757715	6.547430e-05	6	1224	-3.435704	-2.863904	-2.568029	-3926.969981	True
38	NO2(GT)	PT08.S5(O3)	-11.498055	5.446771e-20	-3.905366	-3.341102	-3.0479	-11.493240	4.680783e-21	2	1228	-3.435686	-2.863896	-2.568025	8850.883921	-7.237153	1.926207e-10	5	1225	-3.435699	-2.863902	-2.568028	15060.203145	True
39	NO2(GT)	T	-8.285076	5.769871e-12	-3.905366	-3.341102	-3.0479	-8.281688	4.501830e-13	4	1226	-3.435695	-2.863900	-2.568027	9520.612251	-3.369836	1.203118e-02	20	1210	-3.435766	-2.863932	-2.568043	3489.442167	True
40	NO2(GT)	RH	-8.118876	1.517547e-11	-3.905366	-3.341102	-3.0479	-8.115571	1.193561e-12	4	1226	-3.435695	-2.863900	-2.568027	9518.794113	-8.020461	2.083066e-12	1	1229	-3.435682	-2.863895	-2.568024	6762.194011	True
41	NO2(GT)	AH	-8.265363	6.472569e-12	-3.905366	-3.341102	-3.0479	-8.261984	5.054482e-13	4	1226	-3.435695	-2.863900	-2.568027	9504.021513	-4.276464	4.877980e-04	3	1227	-3.435691	-2.863898	-2.568026	-4257.468169	True
42	PT08.S5(O3)	AH	-6.226827	5.179663e-07	-3.905366	-3.341102	-3.0479	-6.223971	5.142080e-08	6	1224	-3.435704	-2.863904	-2.568029	15311.512143	-3.776070	3.161858e-03	8	1222	-3.435713	-2.863908	-2.568031	-4323.111834	True
43	T	AH	-3.875211	1.072864e-02	-3.905366	-3.341102	-3.0479	-3.875754	2.220712e-03	17	1213	-3.435752	-2.863926	-2.568040	3490.488239	-5.232609	7.539782e-06	2	1228	-3.435686	-2.863896	-2.568025	-4122.831833	True
44	RH	AH	-7.467609	6.350136e-10	-3.905366	-3.341102	-3.0479	-7.464555	5.246078e-11	1	1229	-3.435682	-2.863895	-2.568024	6272.058101	-3.530808	7.230239e-03	2	1228	-3.435686	-2.863896	-2.568025	-5020.681117	True
45	CO(GT)	NMHC(GT)	-1.855580	6.023538e-01	-3.905366	-3.341102	-3.0479	-1.852638	3.546590e-01	23	1207	-3.435779	-2.863938	-2.568046	873.688074	-2.392712	1.438040e-01	23	1207	-3.435779	-2.863938	-2.568046	13055.842895	False
46	CO(GT)	C6H6(GT)	-3.055619	9.756910e-02	-3.905366	-3.341102	-3.0479	-3.054041	3.014665e-02	23	1207	-3.435779	-2.863938	-2.568046	898.938741	-2.726789	6.951626e-02	23	1207	-3.435779	-2.863938	-2.568046	5018.752458	False
47	CO(GT)	PT08.S4(NO2)	-3.798390	1.362297e-02	-3.905366	-3.341102	-3.0479	-3.794999	2.958894e-03	23	1207	-3.435779	-2.863938	-2.568046	1087.193383	-2.571166	9.910429e-02	23	1207	-3.435779	-2.863938	-2.568046	14115.501888	False
48	PT08.S1(CO)	NMHC(GT)	-2.101053	4.758168e-01	-3.905366	-3.341102	-3.0479	-2.103031	2.432977e-01	23	1207	-3.435779	-2.863938	-2.568046	13971.368967	-3.254258	1.705114e-02	23	1207	-3.435779	-2.863938	-2.568046	13847.832224	False
49	PT08.S1(CO)	C6H6(GT)	-3.237862	6.382093e-02	-3.905366	-3.341102	-3.0479	-3.245376	1.750385e-02	23	1207	-3.435779	-2.863938	-2.568046	12533.665247	-3.511271	7.702305e-03	23	1207	-3.435779	-2.863938	-2.568046	4399.520094	False
50	PT08.S1(CO)	PT08.S3(NOx)	-2.991350	1.122760e-01	-3.905366	-3.341102	-3.0479	-3.017573	3.328555e-02	23	1207	-3.435779	-2.863938	-2.568046	13445.216485	-3.919083	1.898807e-03	21	1209	-3.435770	-2.863934	-2.568044	13267.115506	False
51	PT08.S1(CO)	PT08.S4(NO2)	-2.585475	2.427257e-01	-3.905366	-3.341102	-3.0479	-2.591492	9.476848e-02	23	1207	-3.435779	-2.863938	-2.568046	12295.088400	-2.530594	1.082067e-01	23	1207	-3.435779	-2.863938	-2.568046	12949.708352	False
52	PT08.S1(CO)	PT08.S5(O3)	-3.325953	5.126612e-02	-3.905366	-3.341102	-3.0479	-3.334911	1.338829e-02	23	1207	-3.435779	-2.863938	-2.568046	12672.410974	-3.747587	3.491474e-03	22	1208	-3.435775	-2.863936	-2.568045	13724.672889	False
53	PT08.S1(CO)	T	-2.682265	2.060221e-01	-3.905366	-3.341102	-3.0479	-2.681176	7.735272e-02	23	1207	-3.435779	-2.863938	-2.568046	14471.240146	-3.442370	9.596531e-03	23	1207	-3.435779	-2.863938	-2.568046	3621.367722	False
54	PT08.S1(CO)	RH	-2.408601	3.207921e-01	-3.905366	-3.341102	-3.0479	-2.405058	1.403139e-01	23	1207	-3.435779	-2.863938	-2.568046	14436.744366	-6.892502	1.344453e-09	7	1223	-3.435708	-2.863906	-2.568030	6731.522102	False
55	PT08.S1(CO)	AH	-2.623957	2.281110e-01	-3.905366	-3.341102	-3.0479	-2.623650	8.820710e-02	23	1207	-3.435779	-2.863938	-2.568046	14355.945648	-3.225738	1.854235e-02	11	1219	-3.435726	-2.863914	-2.568034	-4136.792988	False
56	NMHC(GT)	C6H6(GT)	-2.747914	1.828206e-01	-3.905366	-3.341102	-3.0479	-2.750385	6.571776e-02	23	1207	-3.435779	-2.863938	-2.568046	13538.402460	-2.011819	2.814151e-01	23	1207	-3.435779	-2.863938	-2.568046	5447.064674	False
57	NMHC(GT)	PT08.S2(NMHC)	-2.998420	1.105816e-01	-3.905366	-3.341102	-3.0479	-3.000364	3.486044e-02	23	1207	-3.435779	-2.863938	-2.568046	13661.991740	-2.291741	1.746456e-01	23	1207	-3.435779	-2.863938	-2.568046	13997.932527	False
58	NMHC(GT)	NOx(GT)	-2.721547	1.919250e-01	-3.905366	-3.341102	-3.0479	-2.727529	6.939446e-02	23	1207	-3.435779	-2.863938	-2.568046	13563.210251	-2.344901	1.578951e-01	23	1207	-3.435779	-2.863938	-2.568046	11225.806048	False
59	NMHC(GT)	NO2(GT)	-2.901441	1.355297e-01	-3.905366	-3.341102	-3.0479	-2.906680	4.457675e-02	23	1207	-3.435779	-2.863938	-2.568046	13939.825696	-2.661601	8.092192e-02	23	1207	-3.435779	-2.863938	-2.568046	9159.217834	False
60	NMHC(GT)	PT08.S4(NO2)	-3.256351	6.099861e-02	-3.905366	-3.341102	-3.0479	-3.258184	1.685429e-02	23	1207	-3.435779	-2.863938	-2.568046	13679.668663	-1.825432	3.679105e-01	23	1207	-3.435779	-2.863938	-2.568046	14477.161825	False
61	NMHC(GT)	PT08.S5(O3)	-2.993166	1.118388e-01	-3.905366	-3.341102	-3.0479	-2.996835	3.519103e-02	23	1207	-3.435779	-2.863938	-2.568046	13832.450803	-2.420251	1.361022e-01	22	1208	-3.435775	-2.863936	-2.568045	15036.689963	False
62	C6H6(GT)	NOx(GT)	-2.905165	1.345027e-01	-3.905366	-3.341102	-3.0479	-2.904350	4.484453e-02	23	1207	-3.435779	-2.863938	-2.568046	5414.277645	-3.332428	1.348973e-02	23	1207	-3.435779	-2.863938	-2.568046	11133.347630	False
63	C6H6(GT)	NO2(GT)	-3.331956	5.049018e-02	-3.905366	-3.341102	-3.0479	-3.327442	1.369550e-02	23	1207	-3.435779	-2.863938	-2.568046	5836.269763	-3.697865	4.143279e-03	23	1207	-3.435779	-2.863938	-2.568046	9142.759318	False
64	C6H6(GT)	RH	-2.869318	1.446224e-01	-3.905366	-3.341102	-3.0479	-2.866057	4.943990e-02	23	1207	-3.435779	-2.863938	-2.568046	6235.586568	-8.067092	1.585559e-12	1	1229	-3.435682	-2.863895	-2.568024	6809.000977	False
65	PT08.S2(NMHC)	NOx(GT)	-3.291918	5.585328e-02	-3.905366	-3.341102	-3.0479	-3.290060	1.532866e-02	23	1207	-3.435779	-2.863938	-2.568046	13845.204011	-3.858865	2.359326e-03	23	1207	-3.435779	-2.863938	-2.568046	11110.083792	False
66	PT08.S2(NMHC)	PT08.S3(NOx)	-3.122902	8.379492e-02	-3.905366	-3.341102	-3.0479	-3.132406	2.424611e-02	23	1207	-3.435779	-2.863938	-2.568046	13234.038489	-3.589283	5.969255e-03	22	1208	-3.435775	-2.863936	-2.568045	13027.504182	False
67	PT08.S2(NMHC)	NO2(GT)	-3.297133	5.512949e-02	-3.905366	-3.341102	-3.0479	-3.291381	1.526817e-02	23	1207	-3.435779	-2.863938	-2.568046	14176.925809	-3.827510	2.638065e-03	23	1207	-3.435779	-2.863938	-2.568046	9019.399241	False
68	PT08.S2(NMHC)	RH	-2.967475	1.181406e-01	-3.905366	-3.341102	-3.0479	-2.964236	3.837195e-02	22	1208	-3.435775	-2.863936	-2.568045	14590.927742	-8.016536	2.131448e-12	1	1229	-3.435682	-2.863895	-2.568024	6791.143865	False
69	NOx(GT)	PT08.S4(NO2)	-3.705533	1.802743e-02	-3.905366	-3.341102	-3.0479	-3.699451	4.120881e-03	23	1207	-3.435779	-2.863938	-2.568046	11191.323799	-2.487027	1.186628e-01	23	1207	-3.435779	-2.863938	-2.568046	14377.141267	False
70	NO2(GT)	PT08.S4(NO2)	-3.467230	3.541309e-02	-3.905366	-3.341102	-3.0479	-3.459714	9.084054e-03	23	1207	-3.435779	-2.863938	-2.568046	9148.729213	-2.226344	1.968235e-01	23	1207	-3.435779	-2.863938	-2.568046	14750.162495	False
71	PT08.S4(NO2)	PT08.S5(O3)	-3.138694	8.079249e-02	-3.905366	-3.341102	-3.0479	-3.134582	2.409758e-02	23	1207	-3.435779	-2.863938	-2.568046	13603.928448	-5.111569	1.328716e-05	9	1221	-3.435717	-2.863910	-2.568032	14147.451420	False
72	PT08.S4(NO2)	T	-2.952195	1.220106e-01	-3.905366	-3.341102	-3.0479	-2.945505	4.030654e-02	22	1208	-3.435775	-2.863936	-2.568045	15132.492318	-3.592002	5.915792e-03	23	1207	-3.435779	-2.863938	-2.568046	3811.074789	False
73	PT08.S4(NO2)	RH	-2.464276	2.950477e-01	-3.905366	-3.341102	-3.0479	-2.457872	1.260639e-01	23	1207	-3.435779	-2.863938	-2.568046	15067.946106	-6.943893	1.008714e-09	7	1223	-3.435708	-2.863906	-2.568030	6755.612209	False
74	PT08.S4(NO2)	AH	-3.498969	3.248692e-02	-3.905366	-3.341102	-3.0479	-3.498135	8.035128e-03	23	1207	-3.435779	-2.863938	-2.568046	14986.157863	-2.481300	1.200908e-01	22	1208	-3.435775	-2.863936	-2.568045	-3513.593070	False
75	PT08.S5(O3)	T	-3.134391	8.160212e-02	-3.905366	-3.341102	-3.0479	-3.130477	2.437844e-02	22	1208	-3.435775	-2.863936	-2.568045	15425.880947	-3.612686	5.523085e-03	17	1213	-3.435752	-2.863926	-2.568040	3593.435133	False
76	PT08.S5(O3)	RH	-2.880129	1.415153e-01	-3.905366	-3.341102	-3.0479	-2.875690	4.824878e-02	22	1208	-3.435775	-2.863936	-2.568045	15385.318515	-6.892642	1.343400e-09	7	1223	-3.435708	-2.863906	-2.568030	6761.987080	False
77	T	RH	-1.903507	5.782269e-01	-3.905366	-3.341102	-3.0479	-1.894857	3.344844e-01	18	1212	-3.435757	-2.863928	-2.568041	1866.712556	-4.352790	3.594512e-04	9	1221	-3.435717	-2.863910	-2.568032	5726.019311	False

Multivariate Cointegration Aanlysis

cointegration for deseasonalized time series

NOTE: Johansen cointegration test using trace test statistic with 5% significance level
H0: the number of cointegration vectors < r
HA: the number of cointegration vectors = r

multivariate rolling variables(window=24): 'PT08.S1(CO)', 'PT08.S2(NMHC)', 'PT08.S3(NOx)', 'PT08.S4(NO2)', 'PT08.S5(O3)'

cointegration rank: 4

	full rank	test statistic	critical value	reject
johansen cointegration rank
1	5	129.988005	69.8189	False
2	5	70.042493	47.8545	False
3	5	37.747946	29.7961	False
4	5	14.346635	15.4943	True

multivariate rolling variables(window=24): 'PT08.S1(CO)', 'PT08.S2(NMHC)', 'PT08.S3(NOx)', 'PT08.S4(NO2)', 'PT08.S5(O3)', 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)'

cointegration rank: 7

	full rank	test statistic	critical value	reject
johansen cointegration rank
1	10	349.008827	239.2468	False
2	10	249.096809	197.3772	False
3	10	188.240041	159.529	False
4	10	142.466241	125.6185	False
5	10	100.865666	95.7542	False
6	10	72.549839	69.8189	False
7	10	45.679593	47.8545	True

multivariate rolling variables(window=24): 'PT08.S1(CO)', 'PT08.S2(NMHC)', 'PT08.S3(NOx)', 'PT08.S4(NO2)', 'PT08.S5(O3)', 'T', 'RH', 'AH'

cointegration rank: 7

	full rank	test statistic	critical value	reject
johansen cointegration rank
1	8	250.292898	159.529	False
2	8	174.561089	125.6185	False
3	8	124.917753	95.7542	False
4	8	80.970664	69.8189	False
5	8	52.055663	47.8545	False
6	8	30.953717	29.7961	False
7	8	13.82569	15.4943	True

multivariate rolling variables(window=24): 'CO(GT)', 'NMHC(GT)', 'C6H6(GT)', 'NOx(GT)', 'NO2(GT)', 'T', 'RH', 'AH'

cointegration rank: 3

	full rank	test statistic	critical value	reject
johansen cointegration rank
1	8	184.007205	159.529	False
2	8	130.236397	125.6185	False
3	8	91.142881	95.7542	True

Cross-Covariance Analysis

'zero-lag' & 'zero-dffierence' cross covariance

: cross covariance is not steady covariance.

Univariate Time Series Characteristic Analysis

Regime Analysis

endog = smt.AutoReg(y, lags=1, trend='ct', seasonal=24).fit().resid

		CO(GT)	PT08.S1(CO)	NMHC(GT)	C6H6(GT)	PT08.S2(NMHC)	NOx(GT)	PT08.S3(NOx)	NO2(GT)	PT08.S4(NO2)	PT08.S5(O3)	T	RH	AH
Evaluation	Dep. Variable:	y	y	y	y	y	y	y	y	y	y	y	y	y
	Model:	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression	MarkovAutoregression
	Date:	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023	Sun, 06 Aug 2023
	Time:	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28	16:10:28
	Sample:	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004	03-10-2004
		- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004	- 05-01-2004
	Covariance Type:	approx	approx	approx	approx	approx	approx	approx	approx	approx	approx	approx	approx	approx
	No. Observations:	1226	1226	1226	1226	1226	1226	1226	1226	1226	1226	1226	1226	1226
	Log Likelihood	-930.211	-7365.290	-6959.116	-3012.664	-7429.182	-5944.079	-7262.418	-4694.032	-7692.651	-7811.766	-1582.347	-3275.844	2496.972
	AIC	1876.421	14746.580	13934.233	6041.327	14874.364	11904.159	14540.835	9404.065	15401.303	15639.533	3180.694	6567.687	-4977.944
	BIC	1917.313	14787.472	13975.125	6082.219	14915.256	11945.051	14581.727	9444.957	15442.195	15680.425	3221.586	6608.579	-4937.052
	HQIC	1891.809	14761.968	13949.620	6056.715	14889.751	11919.546	14556.223	9419.452	15416.690	15654.920	3196.081	6583.075	-4962.557


Parameter	p[0->0]	0.880076	0.428455	0.876458	0.796967	0.426028	0.893698	0.390147	0.981973	0.465543	0.415082	0.901006	0.960652	0.920954
	p[1->0]	0.214701	0.362537	0.170316	0.218055	0.361342	0.161763	0.352856	0.003532	0.37483	0.358166	0.13585	0.198772	0.179942
	sigma2[0]	0.084451	9675.113302	948.035153	1.535768	10737.746091	317.025499	8172.310031	13.687741	16503.04379	20042.703687	0.290376	7.299175	0.000353
	sigma2[1]	0.869331	9674.575384	18974.172769	20.595025	10737.497575	2616.902935	8184.612921	187.285781	16503.30315	20042.829075	1.765689	60.494245	0.004115
	ar.L1	0.183671	0.092349	0.188038	0.128529	0.128017	0.154356	0.181609	0.120595	0.064329	0.147155	0.276113	0.240807	0.269414
	ar.L2	-0.173284	-0.122451	-0.20014	-0.110626	-0.127944	-0.088726	-0.100084	-0.109547	-0.121187	-0.112021	0.041176	-0.01256	-0.083374
	ar.L3	-0.059278	-0.032816	-0.08476	-0.08827	-0.065946	-0.024228	-0.100173	-0.070878	-0.068672	-0.062568	0.017834	0.00195	0.015232
	ar.L4	-0.017732	-0.072015	-0.016172	-0.000896	-0.062958	-0.012737	-0.101756	-0.066468	-0.041504	-0.086943	-0.017472	0.027337	0.015456
	duration[0]	8.33864	1.749642	8.094415	4.925317	1.742246	9.407152	1.63974	55.472493	1.871059	1.709641	10.10161	25.413964	12.650861
	duration[1]	4.657631	2.758343	5.871432	4.586005	2.767463	6.181893	2.834013	283.100248	2.667875	2.792	7.361083	5.030878	5.557336

Volatility Analysis

endog = smt.AutoReg(y, lags=1, trend='ct', seasonal=24).fit().resid + ARX(lags=4, volatility=GARCH(2,2,1), rescale=False); AR - GJR-GARCH Model

	CO(GT)	PT08.S1(CO)	NMHC(GT)	C6H6(GT)	PT08.S2(NMHC)	NOx(GT)	PT08.S3(NOx)	NO2(GT)	PT08.S4(NO2)	PT08.S5(O3)	T	RH	AH
Model
Dep. Variable:	CO(GT)	PT08.S1(CO)	NMHC(GT)	C6H6(GT)	PT08.S2(NMHC)	NOx(GT)	PT08.S3(NOx)	NO2(GT)	PT08.S4(NO2)	PT08.S5(O3)	T	RH	AH
Mean Model:	AR	AR	AR	AR	AR	AR	AR	AR	AR	AR	AR	AR	AR
Vol Model:	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH	GJR-GARCH
Distribution:	Normal	Normal	Normal	Normal	Normal	Normal	Normal	Normal	Normal	Normal	Normal	Normal	Normal
Method:	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood	Maximum Likelihood

Date:	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023	Sun, Aug 06 2023
Time:	16:49:42	16:49:43	16:49:43	16:49:43	16:49:44	16:49:44	16:49:44	16:49:45	16:49:45	16:49:45	16:49:46	16:49:46	16:49:46
R-squared:	0.026	0.027	0.012	0.023	0.039	0.016	0.069	0.005	0.018	0.044	0.080	0.052	0.047
Adj. R-squared:	0.023	0.023	0.009	0.020	0.036	0.013	0.066	0.002	0.015	0.041	0.077	0.049	0.044
Log-Likelihood:	-1044.95	-7343.31	-7150.36	-3085.62	-7390.33	-6020.84	-7232.22	-4732.09	-7627.62	-7795.19	-1625.91	-3322.75	2365.46
AIC:	2111.90	14708.6	14322.7	6193.24	14802.7	12063.7	14486.4	9486.19	15277.2	15612.4	3273.81	6667.49	-4708.93
BIC:	2168.13	14764.8	14378.9	6249.46	14858.9	12119.9	14542.7	9542.41	15333.5	15668.6	3330.04	6723.72	-4652.70
No. Observations:	1226	1226	1226	1226	1226	1226	1226	1226	1226	1226	1226	1226	1226
Df Residuals:	1221	1221	1221	1221	1221	1221	1221	1221	1221	1221	1221	1221	1221
Df Model:	5	5	5	5	5	5	5	5	5	5	5	5	5

			coef	std err	t	P>\|t\|	95.0% Conf. Int.
variable	characteristics type
CO(GT)	Mean	Const	-0.0132	1.515e-02	-0.869	0.385	[-4.286e-02,1.653e-02]
		CO(GT)[1]	0.2175	4.527e-02	4.803	1.561e-06	[ 0.129, 0.306]
		CO(GT)[2]	-0.1925	4.592e-02	-4.192	2.766e-05	[ -0.283, -0.102]
		CO(GT)[3]	-0.0127	3.291e-02	-0.385	0.700	[-7.719e-02,5.184e-02]
		CO(GT)[4]	-0.0229	3.475e-02	-0.660	0.509	[-9.105e-02,4.517e-02]
PT08.S1(CO)	Mean	Const	0.9198	3.047	0.302	0.763	[ -5.053, 6.892]
		PT08...CO)[1]	0.1306	3.456e-02	3.779	1.574e-04	[6.286e-02, 0.198]
		PT08...CO)[2]	-0.1122	3.132e-02	-3.583	3.395e-04	[ -0.174,-5.084e-02]
		PT08...CO)[3]	-0.0277	3.272e-02	-0.846	0.398	[-9.181e-02,3.646e-02]
		PT08...CO)[4]	-0.0566	2.492e-02	-2.269	2.324e-02	[ -0.105,-7.714e-03]
NMHC(GT)	Mean	Const	-1.2142	2.567	-0.473	0.636	[ -6.245, 3.816]
		NMHC(GT)[1]	0.2326	6.858e-02	3.392	6.940e-04	[9.820e-02, 0.367]
		NMHC(GT)[2]	-0.2214	5.068e-02	-4.368	1.252e-05	[ -0.321, -0.122]
		NMHC(GT)[3]	-5.9363e-03	4.593e-02	-0.129	0.897	[-9.596e-02,8.409e-02]
		NMHC(GT)[4]	-0.0450	3.409e-02	-1.320	0.187	[ -0.112,2.183e-02]
C6H6(GT)	Mean	Const	0.0156	7.820e-02	0.199	0.842	[ -0.138, 0.169]
		C6H6(GT)[1]	0.2141	4.681e-02	4.575	4.771e-06	[ 0.122, 0.306]
		C6H6(GT)[2]	-0.1480	3.487e-02	-4.245	2.187e-05	[ -0.216,-7.968e-02]
		C6H6(GT)[3]	-0.0592	2.376e-02	-2.493	1.265e-02	[ -0.106,-1.267e-02]
		C6H6(GT)[4]	-3.6311e-03	2.243e-02	-0.162	0.871	[-4.760e-02,4.034e-02]
PT08.S2(NMHC)	Mean	Const	1.5523	2.763	0.562	0.574	[ -3.864, 6.968]
		PT08...HC)[1]	0.1625	3.585e-02	4.532	5.840e-06	[9.222e-02, 0.233]
		PT08...HC)[2]	-0.1342	2.936e-02	-4.571	4.847e-06	[ -0.192,-7.668e-02]
		PT08...HC)[3]	-0.0695	2.577e-02	-2.696	7.016e-03	[ -0.120,-1.897e-02]
		PT08...HC)[4]	-0.0288	2.605e-02	-1.105	0.269	[-7.984e-02,2.227e-02]
NOx(GT)	Mean	Const	-0.4985	1.027	-0.485	0.627	[ -2.512, 1.514]
		NOx(GT)[1]	0.1356	4.180e-02	3.243	1.183e-03	[5.364e-02, 0.218]
		NOx(GT)[2]	-0.1055	3.981e-02	-2.649	8.073e-03	[ -0.183,-2.743e-02]
		NOx(GT)[3]	-0.0620	3.784e-02	-1.638	0.101	[ -0.136,1.217e-02]
		NOx(GT)[4]	-0.0337	3.955e-02	-0.852	0.394	[ -0.111,4.382e-02]
PT08.S3(NOx)	Mean	Const	-2.9614	2.683	-1.104	0.270	[ -8.220, 2.298]
		PT08...Ox)[1]	0.1586	3.192e-02	4.968	6.767e-07	[9.601e-02, 0.221]
		PT08...Ox)[2]	-0.0970	3.147e-02	-3.084	2.044e-03	[ -0.159,-3.536e-02]
		PT08...Ox)[3]	-0.1078	3.045e-02	-3.542	3.973e-04	[ -0.168,-4.817e-02]
		PT08...Ox)[4]	-0.1017	3.004e-02	-3.385	7.110e-04	[ -0.161,-4.282e-02]
NO2(GT)	Mean	Const	-0.1453	0.272	-0.535	0.593	[ -0.678, 0.387]
		NO2(GT)[1]	0.0610	3.600e-02	1.696	8.998e-02	[-9.521e-03, 0.132]
		NO2(GT)[2]	-0.0943	3.248e-02	-2.904	3.686e-03	[ -0.158,-3.066e-02]
		NO2(GT)[3]	-0.0505	3.376e-02	-1.496	0.135	[ -0.117,1.568e-02]
		NO2(GT)[4]	-0.0574	3.011e-02	-1.907	5.650e-02	[ -0.116,1.591e-03]
PT08.S4(NO2)	Mean	Const	1.0498	3.409	0.308	0.758	[ -5.631, 7.731]
		PT08...O2)[1]	0.1493	4.324e-02	3.452	5.572e-04	[6.451e-02, 0.234]
		PT08...O2)[2]	-0.1248	3.086e-02	-4.042	5.299e-05	[ -0.185,-6.426e-02]
		PT08...O2)[3]	-0.0599	2.494e-02	-2.400	1.638e-02	[ -0.109,-1.098e-02]
		PT08...O2)[4]	-8.6271e-03	2.357e-02	-0.366	0.714	[-5.482e-02,3.757e-02]
PT08.S5(O3)	Mean	Const	0.3936	12.089	3.256e-02	0.974	[-23.301, 24.089]
		PT08...O3)[1]	0.1976	4.808e-02	4.110	3.955e-05	[ 0.103, 0.292]
		PT08...O3)[2]	-0.1282	3.233e-02	-3.966	7.307e-05	[ -0.192,-6.487e-02]
		PT08...O3)[3]	-0.0413	6.376e-02	-0.648	0.517	[ -0.166,8.368e-02]
		PT08...O3)[4]	-0.0695	4.573e-02	-1.521	0.128	[ -0.159,2.009e-02]
T	Mean	Const	-2.9876e-04	2.519e-02	-1.186e-02	0.991	[-4.967e-02,4.908e-02]
		T[1]	0.2962	4.306e-02	6.880	5.997e-12	[ 0.212, 0.381]
		T[2]	-0.0314	4.427e-02	-0.709	0.478	[ -0.118,5.535e-02]
		T[3]	0.0495	3.918e-02	1.264	0.206	[-2.726e-02, 0.126]
		T[4]	-0.0396	3.018e-02	-1.313	0.189	[-9.876e-02,1.953e-02]
RH	Mean	Const	0.0186	0.103	0.180	0.857	[ -0.184, 0.221]
		RH[1]	0.2422	3.983e-02	6.081	1.192e-09	[ 0.164, 0.320]
		RH[2]	-0.0514	5.091e-02	-1.010	0.313	[ -0.151,4.837e-02]
		RH[3]	0.0544	4.568e-02	1.191	0.234	[-3.514e-02, 0.144]
		RH[4]	-0.0181	3.271e-02	-0.555	0.579	[-8.226e-02,4.596e-02]
AH	Mean	Const	-3.8408e-04	1.721e-03	-0.223	0.823	[-3.757e-03,2.989e-03]
		AH[1]	0.2611	4.776e-02	5.467	4.584e-08	[ 0.167, 0.355]
		AH[2]	-0.1206	4.646e-02	-2.596	9.430e-03	[ -0.212,-2.955e-02]
		AH[3]	0.0233	4.310e-02	0.541	0.588	[-6.116e-02, 0.108]
		AH[4]	0.0146	4.965e-02	0.294	0.769	[-8.272e-02, 0.112]
CO(GT)	Volatility	omega	0.0177	3.048e-02	0.581	0.561	[-4.203e-02,7.746e-02]
		alpha[1]	0.1239	7.244e-02	1.711	8.716e-02	[-1.806e-02, 0.266]
		alpha[2]	0.0000	0.108	0.000	1.000	[ -0.212, 0.212]
		gamma[1]	-0.0942	0.147	-0.640	0.522	[ -0.383, 0.194]
		beta[1]	0.5241	0.708	0.740	0.459	[ -0.864, 1.913]
		beta[2]	0.3452	0.561	0.615	0.539	[ -0.755, 1.446]
PT08.S1(CO)	Volatility	omega	4837.4131	3873.570	1.249	0.212	[-2.755e+03,1.243e+04]
		alpha[1]	0.2050	0.139	1.473	0.141	[-6.786e-02, 0.478]
		alpha[2]	6.2117e-12	4.262e-02	1.458e-10	1.000	[-8.353e-02,8.353e-02]
		gamma[1]	-0.1817	0.100	-1.815	6.956e-02	[ -0.378,1.454e-02]
		beta[1]	0.3744	0.482	0.777	0.437	[ -0.571, 1.319]
		beta[2]	3.5600e-13	0.898	3.965e-13	1.000	[ -1.760, 1.760]
NMHC(GT)	Volatility	omega	3565.6077	1569.228	2.272	2.307e-02	[4.900e+02,6.641e+03]
		alpha[1]	0.7221	0.226	3.198	1.382e-03	[ 0.280, 1.165]
		alpha[2]	0.1757	0.283	0.621	0.535	[ -0.379, 0.730]
		gamma[1]	-0.5062	0.203	-2.492	1.271e-02	[ -0.904, -0.108]
		beta[1]	0.0000	0.499	0.000	1.000	[ -0.977, 0.977]
		beta[2]	0.0639	0.140	0.457	0.648	[ -0.210, 0.338]
C6H6(GT)	Volatility	omega	4.5609	1.028	4.437	9.105e-06	[ 2.546, 6.575]
		alpha[1]	0.8608	0.245	3.517	4.360e-04	[ 0.381, 1.340]
		alpha[2]	0.0000	9.654e-02	0.000	1.000	[ -0.189, 0.189]
		gamma[1]	-0.5263	0.177	-2.971	2.969e-03	[ -0.874, -0.179]
		beta[1]	0.1196	0.133	0.897	0.370	[ -0.142, 0.381]
		beta[2]	0.0000	5.046e-02	0.000	1.000	[-9.890e-02,9.890e-02]
PT08.S2(NMHC)	Volatility	omega	5896.4065	1320.354	4.466	7.978e-06	[3.309e+03,8.484e+03]
		alpha[1]	0.3639	8.802e-02	4.134	3.563e-05	[ 0.191, 0.536]
		alpha[2]	8.9518e-13	6.096e-02	1.469e-11	1.000	[ -0.119, 0.119]
		gamma[1]	-0.1607	6.589e-02	-2.440	1.471e-02	[ -0.290,-3.160e-02]
		beta[1]	0.1893	0.201	0.940	0.347	[ -0.205, 0.584]
		beta[2]	2.3487e-12	0.110	2.133e-11	1.000	[ -0.216, 0.216]
NOx(GT)	Volatility	omega	25.1199	33.212	0.756	0.449	[-39.975, 90.214]
		alpha[1]	0.0989	4.605e-02	2.148	3.175e-02	[8.637e-03, 0.189]
		alpha[2]	1.2340e-13	5.605e-02	2.202e-12	1.000	[ -0.110, 0.110]
		gamma[1]	-0.0134	0.100	-0.133	0.894	[ -0.210, 0.183]
		beta[1]	0.1890	0.129	1.460	0.144	[-6.476e-02, 0.443]
		beta[2]	0.7009	0.116	6.016	1.783e-09	[ 0.473, 0.929]
PT08.S3(NOx)	Volatility	omega	2454.0247	1954.886	1.255	0.209	[-1.377e+03,6.286e+03]
		alpha[1]	0.2455	7.112e-02	3.451	5.583e-04	[ 0.106, 0.385]
		alpha[2]	0.0576	9.412e-02	0.612	0.540	[ -0.127, 0.242]
		gamma[1]	-0.1941	7.508e-02	-2.585	9.742e-03	[ -0.341,-4.692e-02]
		beta[1]	0.2029	0.316	0.642	0.521	[ -0.417, 0.822]
		beta[2]	0.2946	0.113	2.617	8.859e-03	[7.401e-02, 0.515]
NO2(GT)	Volatility	omega	1.3273	0.983	1.350	0.177	[ -0.599, 3.254]
		alpha[1]	0.1663	4.701e-02	3.538	4.026e-04	[7.420e-02, 0.258]
		alpha[2]	7.1748e-09	0.116	6.185e-08	1.000	[ -0.227, 0.227]
		gamma[1]	-0.0188	3.703e-02	-0.509	0.611	[-9.141e-02,5.373e-02]
		beta[1]	0.4981	0.620	0.804	0.422	[ -0.717, 1.713]
		beta[2]	0.3450	0.539	0.640	0.522	[ -0.712, 1.402]
PT08.S4(NO2)	Volatility	omega	9219.9300	1976.741	4.664	3.098e-06	[5.346e+03,1.309e+04]
		alpha[1]	0.5076	0.135	3.751	1.761e-04	[ 0.242, 0.773]
		alpha[2]	7.5450e-12	6.056e-02	1.246e-10	1.000	[ -0.119, 0.119]
		gamma[1]	-0.2908	0.131	-2.216	2.669e-02	[ -0.548,-3.361e-02]
		beta[1]	0.1184	0.169	0.702	0.483	[ -0.212, 0.449]
		beta[2]	2.2014e-12	6.307e-02	3.490e-11	1.000	[ -0.124, 0.124]
PT08.S5(O3)	Volatility	omega	1.0021e+04	3.009e+04	0.333	0.739	[-4.896e+04,6.900e+04]
		alpha[1]	0.2182	0.132	1.652	9.844e-02	[-4.060e-02, 0.477]
		alpha[2]	1.6768e-13	0.692	2.422e-13	1.000	[ -1.357, 1.357]
		gamma[1]	-0.1001	5.897e-02	-1.697	8.977e-02	[ -0.216,1.553e-02]
		beta[1]	0.3364	0.361	0.933	0.351	[ -0.370, 1.043]
		beta[2]	6.7762e-13	1.940	3.492e-13	1.000	[ -3.803, 3.803]
T	Volatility	omega	0.3046	7.903e-02	3.854	1.160e-04	[ 0.150, 0.460]
		alpha[1]	0.2030	6.964e-02	2.914	3.564e-03	[6.646e-02, 0.339]
		alpha[2]	0.1384	7.641e-02	1.811	7.016e-02	[-1.139e-02, 0.288]
		gamma[1]	0.1468	6.618e-02	2.218	2.658e-02	[1.706e-02, 0.276]
		beta[1]	1.1683e-11	0.162	7.193e-11	1.000	[ -0.318, 0.318]
		beta[2]	0.2960	8.868e-02	3.337	8.454e-04	[ 0.122, 0.470]
RH	Volatility	omega	4.5112	1.034	4.363	1.282e-05	[ 2.485, 6.538]
		alpha[1]	0.3636	9.310e-02	3.906	9.398e-05	[ 0.181, 0.546]
		alpha[2]	0.1869	8.597e-02	2.174	2.967e-02	[1.844e-02, 0.355]
		gamma[1]	-0.2554	7.789e-02	-3.278	1.044e-03	[ -0.408, -0.103]
		beta[1]	7.4700e-10	0.187	3.991e-09	1.000	[ -0.367, 0.367]
		beta[2]	0.3207	0.140	2.295	2.172e-02	[4.684e-02, 0.595]
AH	Volatility	omega	4.6079e-04	4.063e-04	1.134	0.257	[-3.355e-04,1.257e-03]
		alpha[1]	0.1009	3.929e-02	2.568	1.022e-02	[2.390e-02, 0.178]
		alpha[2]	0.1004	0.240	0.418	0.676	[ -0.371, 0.571]
		gamma[1]	0.1988	0.259	0.767	0.443	[ -0.309, 0.707]
		beta[1]	0.1998	0.640	0.312	0.755	[ -1.054, 1.453]
		beta[2]	0.1998	0.254	0.786	0.432	[ -0.299, 0.698]

Autocorrelation Analysis

ACF and PACF

Autocorrelation for differencing (D=1, d=1, m=24)

	CO(GT)						PT08.S1(CO)						NMHC(GT)						C6H6(GT)						PT08.S2(NMHC)						NOx(GT)						PT08.S3(NOx)						NO2(GT)						PT08.S4(NO2)						PT08.S5(O3)						T						RH						AH
	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination	ref:acov	ref:pacorr	acorr	stats	p-val	determination
lag0	0.737012	1.0	1.0	6.163896	0.013038	True	17538.287069	1.0	1.0	3.552425	0.059458	False	17726.064155	1.0	1.0	5.37914	0.020379	True	18.703476	1.0	1.0	5.1543	0.023189	True	18759.327043	1.0	1.0	2.006677	0.156608	False	2534.369073	1.0	1.0	1.938377	0.163845	False	15816.425965	1.0	1.0	3.180219	0.074535	False	321.789689	1.0	1.0	11.337678	0.00076	True	29980.260228	1.0	1.0	12.008053	0.00053	True	39172.865313	1.0	1.0	1.752227	0.185597	False	1.885387	1.0	1.0	43.543333	0.0	True	34.84285	1.0	1.0	47.325554	0.0	True	0.003098	1.0	1.0	48.856119	0.0	True
lag1	-0.052625	-0.071462	-0.071403	49.113444	0.0	True	-950.683719	-0.054251	-0.054206	34.99744	0.0	True	-1182.374765	-0.066758	-0.066703	52.311442	0.0	True	-1.221219	-0.065348	-0.065294	38.372532	0.0	True	-764.26223	-0.040774	-0.04074	26.239749	0.000002	True	-101.478816	-0.040074	-0.040041	39.692093	0.0	True	811.191314	0.05133	0.051288	20.078824	0.000044	True	-31.161659	-0.096919	-0.096839	46.773112	0.0	True	-2987.84526	-0.099743	-0.09966	39.6927	0.0	True	1491.30659	0.038101	0.03807	25.047398	0.000004	True	0.357806	0.189936	0.189779	43.881213	0.0	True	6.893629	0.198013	0.197849	47.534531	0.0	True	0.000623	0.20119	0.201023	61.849397	0.0	True
lag2	-0.138855	-0.194817	-0.188402	63.412334	0.0	True	-2827.28245	-0.164903	-0.161206	47.800784	0.0	True	-3491.036302	-0.202631	-0.196944	66.33416	0.0	True	-3.098965	-0.170965	-0.165689	57.948788	0.0	True	-2654.774326	-0.143654	-0.141518	43.78898	0.0	True	-447.667779	-0.178825	-0.176639	52.345664	0.0	True	-1869.131657	-0.121327	-0.118177	49.391281	0.0	True	-55.067724	-0.182522	-0.17113	54.410695	0.0	True	-4534.830004	-0.163083	-0.151261	53.802565	0.0	True	-5435.311141	-0.140638	-0.138752	49.1044	0.0	True	0.031506	-0.020061	0.01671	44.657789	0.0	True	0.457898	-0.027109	0.013142	50.920151	0.0	True	-0.000321	-0.150361	-0.103625	67.276734	0.0	True
lag3	-0.080085	-0.145192	-0.108662	80.631299	0.0	True	-1803.327384	-0.126017	-0.102822	68.527366	0.0	True	-1907.454155	-0.143758	-0.107607	82.624071	0.0	True	-2.378005	-0.156556	-0.127142	69.147991	0.0	True	-2258.249875	-0.13618	-0.12038	62.924353	0.0	True	-259.061032	-0.122093	-0.102219	82.902653	0.0	True	-2460.708455	-0.145445	-0.155579	87.554728	0.0	True	-25.554993	-0.122126	-0.079415	74.926652	0.0	True	-3236.104442	-0.147401	-0.107941	68.072641	0.0	True	-5521.178493	-0.13271	-0.140944	70.332718	0.0	True	-0.047744	-0.025758	-0.025323	44.681019	0.0	True	-1.842292	-0.052407	-0.052874	50.927943	0.0	True	-0.000207	-0.013689	-0.066945	69.718787	0.0	True
lag4	-0.087846	-0.19366	-0.119192	80.631519	0.0	True	-2293.486173	-0.182928	-0.13077	69.415748	0.0	True	-2055.023499	-0.192492	-0.115932	82.812628	0.0	True	-1.797881	-0.159293	-0.096126	69.427149	0.0	True	-2357.115381	-0.167645	-0.12565	62.95946	0.0	True	-402.411383	-0.214211	-0.158782	82.930497	0.0	True	-2806.578919	-0.184758	-0.177447	94.364314	0.0	True	-41.86616	-0.198191	-0.130104	75.699105	0.0	True	-3253.071825	-0.176101	-0.108507	68.084009	0.0	True	-5184.277562	-0.148684	-0.132344	72.230234	0.0	True	-0.008254	0.005875	-0.004378	51.677494	0.0	True	0.088345	0.024903	0.002536	58.555965	0.0	True	-0.000139	-0.04497	-0.044887	71.266103	0.0	True
lag5	-0.000314	-0.099489	-0.000426	80.815052	0.0	True	-474.625968	-0.103023	-0.027062	69.451831	0.0	True	-221.00259	-0.112609	-0.012468	82.859092	0.0	True	0.283734	-0.068866	0.01517	69.728816	0.0	True	-100.920285	-0.070205	-0.00538	63.035955	0.0	True	-12.142112	-0.083395	-0.004791	83.117336	0.0	True	-1185.040275	-0.108333	-0.074925	95.038818	0.0	True	8.120312	-0.065356	0.025235	75.983375	0.0	True	91.777355	-0.089284	0.003061	68.175089	0.0	True	-1549.324595	-0.077848	-0.039551	73.143856	0.0	True	-0.143187	-0.079408	-0.075946	71.029727	0.0	True	-2.76302	-0.089012	-0.079299	64.954242	0.0	True	-0.000111	-0.029053	-0.035715	71.282056	0.0	True
lag6	0.009062	-0.09687	0.012295	80.904878	0.0	True	95.614679	-0.088009	0.005452	69.74926	0.0	True	109.662433	-0.109188	0.006187	82.873872	0.0	True	-0.294829	-0.100193	-0.015763	70.131362	0.0	True	-148.907228	-0.084777	-0.007938	63.037163	0.0	True	-31.440349	-0.120977	-0.012406	83.879986	0.0	True	372.807059	-0.047119	0.023571	97.691537	0.0	True	4.924028	-0.074736	0.015302	76.138517	0.0	True	259.675	-0.081631	0.008662	68.23488	0.0	True	-1074.61328	-0.093421	-0.027433	73.346024	0.0	True	-0.23804	-0.102597	-0.126255	91.775743	0.0	True	-2.529465	-0.04488	-0.072596	83.454621	0.0	True	-0.000011	-0.001151	-0.003625	72.597799	0.0	True
lag7	-0.006337	-0.097095	-0.008598	85.203179	0.0	True	274.397996	-0.064377	0.015646	70.921132	0.0	True	-61.821501	-0.102148	-0.003488	83.451984	0.0	True	-0.340434	-0.089945	-0.018202	72.926253	0.0	True	18.706093	-0.065399	0.000997	65.296565	0.0	True	63.494347	-0.059731	0.025053	87.134898	0.0	True	739.020414	-0.03617	0.046725	97.719562	0.0	True	-3.636128	-0.071159	-0.0113	76.151424	0.0	True	210.307732	-0.066235	0.007015	71.153222	0.0	True	505.293117	-0.049076	0.012899	73.42871	0.0	True	-0.24636	-0.093128	-0.130668	95.346259	0.0	True	-4.299386	-0.104102	-0.123394	92.565783	0.0	True	-0.000102	-0.046511	-0.032907	77.366577	0.0	True
lag8	-0.043817	-0.150763	-0.059452	85.275192	0.0	True	-544.438301	-0.105084	-0.031043	73.170773	0.0	True	-386.491353	-0.118468	-0.021804	84.929925	0.0	True	-0.896656	-0.122254	-0.047941	73.410712	0.0	True	-808.60289	-0.106831	-0.043104	66.005137	0.0	True	-131.117528	-0.148242	-0.051736	89.322231	0.0	True	75.928346	-0.06532	0.004801	98.053553	0.0	True	-1.048378	-0.064148	-0.003258	76.166544	0.0	True	-1468.672093	-0.115216	-0.048988	72.671421	0.0	True	-323.015766	-0.071217	-0.008246	73.507898	0.0	True	-0.102162	-0.019793	-0.054186	96.454575	0.0	True	-3.015934	-0.056306	-0.086558	96.459236	0.0	True	-0.000194	-0.053865	-0.062622	78.184954	0.0	True
lag9	-0.005669	-0.107185	-0.007692	100.733605	0.0	True	-754.021483	-0.112369	-0.042993	77.162668	0.0	True	617.704521	-0.051586	0.034847	85.785081	0.0	True	-0.373157	-0.101926	-0.019951	78.419276	0.0	True	-452.636236	-0.082865	-0.024129	68.105222	0.0	True	-107.440313	-0.122749	-0.042393	104.111781	0.0	True	-262.008726	-0.058037	-0.016566	98.876042	0.0	True	-1.134204	-0.045852	-0.003525	76.305154	0.0	True	-1058.862624	-0.107398	-0.035319	75.600919	0.0	True	315.975468	-0.037052	0.008066	74.615339	0.0	True	-0.056895	-0.02511	-0.030177	100.596646	0.0	True	-1.970703	-0.036607	-0.05656	98.455342	0.0	True	-0.00008	-0.013841	-0.025931	78.721289	0.0	True
lag10	0.083026	0.017118	0.112653	102.231016	0.0	True	1004.003358	-0.014985	0.057246	77.412537	0.0	True	469.670873	-0.046375	0.026496	85.96606	0.0	True	1.199326	-0.024556	0.064123	82.924341	0.0	True	778.922189	-0.023311	0.041522	69.13319	0.0	True	279.258123	0.015387	0.110188	104.115985	0.0	True	-410.990413	-0.051631	-0.025985	101.055261	0.0	True	-3.432637	-0.052928	-0.010667	76.390433	0.0	True	1470.24773	-0.031025	0.049041	76.965445	0.0	True	1181.147719	-0.010737	0.030152	75.050302	0.0	True	-0.109943	-0.06343	-0.058313	109.140713	0.0	True	-1.410471	-0.044812	-0.040481	107.262913	0.0	True	-0.000065	-0.034233	-0.020983	84.243052	0.0	True
lag11	-0.02583	-0.100605	-0.035047	102.23351	0.0	True	251.084721	-0.04574	0.014316	77.425915	0.0	True	215.974668	-0.031639	0.012184	87.375121	0.0	True	1.136972	-0.000907	0.060789	82.947067	0.0	True	544.7335	-0.024077	0.029038	69.145678	0.0	True	4.706126	-0.064609	0.001857	104.126419	0.0	True	-668.706701	-0.070023	-0.042279	101.150002	0.0	True	-2.691346	-0.051539	-0.008364	77.14217	0.0	True	1003.004937	-0.026702	0.033456	77.28177	0.0	True	739.926393	-0.008984	0.018889	76.941524	0.0	True	-0.157837	-0.084849	-0.083716	110.243408	0.0	True	-2.961547	-0.089641	-0.084997	108.024662	0.0	True	-0.000208	-0.07406	-0.0673	84.336634	0.0	True
lag12	0.001054	-0.041761	0.00143	106.35651	0.0	True	-58.073707	-0.045762	-0.003311	77.459864	0.0	True	-602.382299	-0.069774	-0.033983	87.412476	0.0	True	-0.080719	-0.032004	-0.004316	85.394601	0.0	True	60.012594	-0.035708	0.003199	69.58815	0.0	True	-7.411247	-0.044892	-0.002924	104.513109	0.0	True	139.370819	-0.027008	0.008812	103.028519	0.0	True	-7.987301	-0.070316	-0.024821	77.853386	0.0	True	482.722219	-0.022899	0.016101	77.934344	0.0	True	-1542.238502	-0.059435	-0.03937	76.941759	0.0	True	-0.056679	-0.032902	-0.030062	110.700119	0.0	True	-0.870592	-0.018887	-0.024986	108.0327	0.0	True	-0.000027	0.006718	-0.008758	89.789509	0.0	True
lag13	0.042825	0.025319	0.058106	110.953309	0.0	True	92.472266	-0.033517	0.005273	78.483948	0.0	True	98.03982	-0.020957	0.005531	88.126445	0.0	True	-0.837336	-0.054063	-0.044769	85.830825	0.0	True	-357.086393	-0.043181	-0.019035	70.044997	0.0	True	45.098732	-0.018576	0.017795	110.198849	0.0	True	620.338871	-0.006679	0.039221	103.385381	0.0	True	7.765795	-0.021979	0.024133	78.005593	0.0	True	-693.048156	-0.045145	-0.023117	78.083011	0.0	True	17.18481	-0.003836	0.000439	78.451158	0.0	True	-0.036462	-0.046356	-0.019339	111.009519	0.0	True	0.089392	-0.019431	0.002566	108.443923	0.0	True	0.000207	0.044956	0.066823	89.811639	0.0	True
lag14	-0.045199	-0.063115	-0.061328	111.393957	0.0	True	507.675279	0.013786	0.028947	78.518265	0.0	True	428.432905	-0.003022	0.02417	90.597783	0.0	True	0.353352	0.010033	0.018892	86.19516	0.0	True	362.688727	0.00552	0.019334	70.18412	0.0	True	-172.859947	-0.080022	-0.068206	110.552445	0.0	True	270.264736	-0.02299	0.017088	103.390537	0.0	True	3.591039	-0.029964	0.01116	78.005598	0.0	True	330.653344	0.000755	0.011029	78.083053	0.0	True	1376.633632	0.022654	0.035143	78.625458	0.0	True	-0.029998	-0.038312	-0.015911	112.155555	0.0	True	-0.639122	-0.05742	-0.018343	109.349183	0.0	True	-0.000013	-0.043826	-0.004255	90.150502	0.0	True
lag15	-0.013988	-0.040208	-0.01898	111.428295	0.0	True	-92.895502	-0.012295	-0.005297	79.669205	0.0	True	-796.75938	-0.064129	-0.044948	91.988842	0.0	True	-0.322791	-0.035363	-0.017258	86.728023	0.0	True	-200.062117	-0.026241	-0.010665	70.576211	0.0	True	43.089607	-0.013612	0.017002	110.553911	0.0	True	-32.47353	-0.027092	-0.002053	103.612112	0.0	True	0.02175	-0.026421	0.000068	78.057782	0.0	True	-5.576379	-0.007672	-0.000186	78.612362	0.0	True	-467.609822	-0.023657	-0.011937	80.088523	0.0	True	-0.05771	-0.050774	-0.030609	112.604577	0.0	True	0.947871	0.015384	0.027204	115.9993	0.0	True	0.000052	0.032389	0.016644	92.065404	0.0	True
lag16	-0.003903	-0.042908	-0.005296	111.441938	0.0	True	-537.749153	-0.034263	-0.030661	80.750401	0.0	True	-597.518554	-0.067769	-0.033708	92.386023	0.0	True	-0.390208	-0.042956	-0.020863	86.988543	0.0	True	-335.719634	-0.033334	-0.017896	71.261153	0.0	True	-2.773208	-0.041998	-0.001094	110.563281	0.0	True	-212.782355	-0.023968	-0.013453	104.684496	0.0	True	-2.100902	-0.033475	-0.006529	78.287831	0.0	True	-623.385182	-0.029908	-0.020793	79.387489	0.0	True	-1354.202201	-0.039232	-0.03457	81.076499	0.0	True	0.036108	-0.00276	0.019151	116.04555	0.0	True	2.567998	0.035576	0.073702	120.261141	0.0	True	0.000123	0.019931	0.039549	92.474573	0.0	True
lag17	0.002459	-0.024515	0.003337	111.507901	0.0	True	-520.982662	-0.046382	-0.029705	81.628516	0.0	True	319.146792	-0.029053	0.018004	93.88877	0.0	True	-0.272726	-0.043529	-0.014582	86.990441	0.0	True	-443.535355	-0.046899	-0.023643	71.29363	0.0	True	-7.008379	-0.038599	-0.002765	110.577085	0.0	True	-467.915179	-0.035318	-0.029584	105.559384	0.0	True	4.40927	-0.000952	0.013702	78.341814	0.0	True	-754.059503	-0.048256	-0.025152	79.422532	0.0	True	-1112.352029	-0.032747	-0.028396	81.969453	0.0	True	0.099914	0.010599	0.052994	131.688717	0.0	True	2.054926	0.00965	0.058977	126.397313	0.0	True	0.000057	0.009135	0.018274	95.007137	0.0	True
lag18	0.005405	-0.023754	0.007334	112.116342	0.0	True	-469.314542	-0.049608	-0.026759	83.632758	0.0	True	620.520882	-0.007351	0.035006	94.239334	0.0	True	-0.023264	-0.026835	-0.001244	87.00744	0.0	True	-96.538758	-0.025899	-0.005146	71.378366	0.0	True	-8.503021	-0.040634	-0.003355	110.58438	0.0	True	-422.460281	-0.040433	-0.02671	106.510153	0.0	True	-2.135007	-0.021639	-0.006635	79.822462	0.0	True	-160.26352	-0.029593	-0.005346	80.166657	0.0	True	-1057.063361	-0.044605	-0.026985	83.609308	0.0	True	0.212943	0.071233	0.112944	132.653433	0.0	True	2.464697	0.039836	0.070738	127.072291	0.0	True	-0.000141	-0.051222	-0.045444	95.025366	0.0	True
lag19	0.01641	-0.003794	0.022265	116.218409	0.0	True	708.729477	0.012293	0.04041	89.217032	0.0	True	299.580762	-0.013921	0.016901	97.726018	0.0	True	0.069608	-0.029493	0.003722	90.609001	0.0	True	155.872917	-0.020799	0.008309	77.080708	0.0	True	6.178892	-0.015629	0.002438	124.283561	0.0	True	440.214274	0.004286	0.027833	115.020234	0.0	True	-11.17677	-0.051953	-0.034733	85.246967	0.0	True	738.204302	0.000503	0.024623	82.576744	0.0	True	1431.878943	0.013477	0.036553	93.309273	0.0	True	0.052859	-0.028306	0.028036	133.850378	0.0	True	0.817103	-0.014272	0.023451	127.478556	0.0	True	0.000012	0.023998	0.003854	98.340544	0.0	True
lag20	0.04259	0.047286	0.057788	116.218553	0.0	True	1182.512564	0.042645	0.067425	89.218636	0.0	True	944.395373	0.048607	0.053277	98.586347	0.0	True	1.012752	0.02908	0.054148	91.512036	0.0	True	1278.142007	0.047613	0.068134	77.551126	0.0	True	267.640834	0.08186	0.105605	125.094278	0.0	True	1316.468336	0.059816	0.083234	119.263196	0.0	True	21.383924	0.047414	0.066453	86.097752	0.0	True	1327.966085	0.03089	0.044295	82.965659	0.0	True	3481.013047	0.062649	0.088863	95.284739	0.0	True	0.058854	0.010118	0.031216	134.770286	0.0	True	0.633656	0.009783	0.018186	127.481887	0.0	True	0.000161	0.044014	0.05195	103.766011	0.0	True
lag21	-0.000252	0.038909	-0.000342	119.386155	0.0	True	-20.028635	0.000085	-0.001142	92.462395	0.0	True	468.917795	0.060819	0.026454	101.695437	0.0	True	0.506905	0.01523	0.027102	94.778064	0.0	True	366.953572	0.012295	0.019561	79.004828	0.0	True	65.081382	0.051234	0.02568	126.894258	0.0	True	929.169499	0.048538	0.058747	125.935322	0.0	True	8.46514	0.03119	0.026306	88.146075	0.0	True	533.230467	0.022956	0.017786	85.092802	0.0	True	1570.261988	0.029448	0.040085	103.298852	0.0	True	0.051573	0.003604	0.027354	134.778076	0.0	True	0.057351	-0.001103	0.001646	130.487331	0.0	True	0.000206	0.055946	0.066431	106.996038	0.0	True
lag22	0.037395	0.104729	0.050738	124.553887	0.0	True	900.492749	0.082501	0.051344	97.514906	0.0	True	891.041049	0.130097	0.050267	101.889645	0.0	True	0.963609	0.075691	0.05152	99.99847	0.0	True	644.798049	0.059331	0.034372	83.602135	0.0	True	96.933166	0.10515	0.038247	128.99422	0.0	True	1164.686974	0.10088	0.073638	128.423228	0.0	True	13.129255	0.075061	0.040801	106.174367	0.0	True	1246.529192	0.073991	0.041578	93.276538	0.0	True	3161.417198	0.114938	0.080704	103.784814	0.0	True	-0.004744	-0.023927	-0.002516	135.148608	0.0	True	-1.722014	-0.054936	-0.049422	136.337897	0.0	True	0.000159	0.035862	0.051236	138.11918	0.0	True
lag23	0.047743	0.148962	0.064779	412.743913	0.0	True	1123.378315	0.129563	0.064053	325.965764	0.0	True	222.603045	0.121787	0.012558	387.901269	0.0	True	1.217754	0.129267	0.065108	325.015217	0.0	True	1146.183748	0.109522	0.061099	298.497531	0.0	True	104.655193	0.135696	0.041294	417.912292	0.0	True	710.903382	0.108864	0.044947	356.290965	0.0	True	38.934505	0.189125	0.120994	372.159123	0.0	True	2443.973308	0.157568	0.081519	325.725552	0.0	True	778.165134	0.072124	0.019865	352.871297	0.0	True	-0.032704	-0.002426	-0.017346	393.473719	0.0	True	-2.401584	-0.03469	-0.068926	397.29468	0.0	True	-0.000492	-0.174069	-0.158974	406.154378	0.0	True
lag24	-0.356382	-0.452621	-0.48355	420.460757	0.0	True	-7550.66477	-0.419618	-0.430525	329.877006	0.0	True	-8538.975666	-0.454595	-0.481719	401.883191	0.0	True	-7.991557	-0.414726	-0.427277	330.410596	0.0	True	-7833.077578	-0.4122	-0.417556	303.796284	0.0	True	-1227.040315	-0.443222	-0.48416	418.752345	0.0	True	-6800.665125	-0.402005	-0.429975	356.318099	0.0	True	-149.486549	-0.423435	-0.464547	372.159192	0.0	True	-13019.696769	-0.409561	-0.434276	332.245798	0.0	True	-17610.108707	-0.437084	-0.449549	353.477729	0.0	True	-0.863148	-0.488434	-0.45781	400.190162	0.0	True	-16.032439	-0.477307	-0.460136	404.744811	0.0	True	-0.001445	-0.419304	-0.466334	410.181786	0.0	True
lag25	0.058292	0.024763	0.079093	431.719297	0.0	True	987.557305	0.017742	0.056309	341.095589	0.0	True	1887.181121	0.050046	0.106464	416.61146	0.0	True	1.236947	0.019143	0.066135	340.631363	0.0	True	1229.481226	0.045266	0.06554	312.615486	0.0	True	66.136452	-0.006854	0.026096	435.752164	0.0	True	74.179503	0.103663	0.00469	358.694602	0.0	True	-0.076192	-0.059727	-0.000237	391.111547	0.0	True	2179.642199	-0.002851	0.072703	340.436465	0.0	True	-868.548226	0.037217	-0.022172	358.357519	0.0	True	-0.13912	0.121221	-0.073788	400.322818	0.0	True	-2.707781	0.114219	-0.077714	404.764392	0.0	True	-0.000177	0.104213	-0.057139	412.67764	0.0	True
lag26	0.07038	-0.099986	0.095494	436.762719	0.0	True	1671.822098	-0.035145	0.095324	344.066964	0.0	True	1936.074401	-0.084515	0.109222	420.329892	0.0	True	1.701759	-0.036094	0.090986	344.702081	0.0	True	1585.498361	-0.024489	0.084518	315.887553	0.0	True	297.389683	-0.063226	0.117343	438.931762	0.0	True	693.923115	-0.024795	0.043874	360.480973	0.0	True	39.869206	-0.037988	0.123898	393.224036	0.0	True	2441.905853	-0.043888	0.08145	341.068273	0.0	True	2462.74697	-0.029826	0.062869	364.529127	0.0	True	0.019543	-0.022195	0.010366	403.098863	0.0	True	-0.13876	-0.043683	-0.003982	411.226531	0.0	True	0.000139	-0.087692	0.044962	412.689431	0.0	True
lag27	0.047085	-0.046587	0.063887	449.789847	0.0	True	860.034103	-0.029681	0.049038	349.986166	0.0	True	972.393428	-0.047576	0.054857	430.399444	0.0	True	1.073514	-0.034554	0.057396	347.693129	0.0	True	965.335076	-0.026683	0.051459	320.001678	0.0	True	128.559963	-0.061613	0.050727	450.276081	0.0	True	601.373049	-0.052974	0.038022	365.276269	0.0	True	13.305132	-0.036918	0.041347	404.095385	0.0	True	677.919149	-0.070409	0.022612	348.864195	0.0	True	2768.434889	-0.046495	0.070672	369.085458	0.0	True	0.089364	0.024872	0.047398	403.624252	0.0	True	2.519716	0.030062	0.072317	411.630787	0.0	True	-0.00001	-0.0335	-0.003089	415.259549	0.0	True
lag28	0.075642	-0.015124	0.102634	450.041343	0.0	True	1213.344989	-0.029707	0.069183	350.503452	0.0	True	1599.49513	-0.028337	0.090234	430.432369	0.0	True	0.919813	-0.026256	0.049179	348.939204	0.0	True	1081.985769	-0.028869	0.057677	320.775292	0.0	True	242.730644	-0.058426	0.095776	450.38083	0.0	True	984.876135	-0.054993	0.062269	365.309291	0.0	True	30.170281	-0.028259	0.093758	404.113451	0.0	True	2380.316329	-0.019499	0.079396	349.466105	0.0	True	2377.707662	-0.044975	0.060698	369.447378	0.0	True	-0.03886	-0.039458	-0.020611	410.285534	0.0	True	-0.629952	-0.036485	-0.01808	419.823523	0.0	True	0.000141	0.030612	0.045587	418.832934	0.0	True
lag29	-0.010506	-0.028202	-0.014254	450.833986	0.0	True	-358.536828	-0.04921	-0.020443	350.543475	0.0	True	91.423217	0.001276	0.005158	435.029228	0.0	True	-0.593438	-0.022523	-0.031729	348.970355	0.0	True	-468.986566	-0.025237	-0.025	320.818638	0.0	True	23.314478	-0.013656	0.009199	450.406625	0.0	True	81.693234	-0.060633	0.005165	366.775548	0.0	True	-1.229369	0.000973	-0.00382	405.671822	0.0	True	-661.122568	-0.042437	-0.022052	349.476297	0.0	True	669.843058	-0.01474	0.0171	370.226508	0.0	True	0.138312	0.035896	0.07336	416.519781	0.0	True	2.834714	0.023005	0.081357	421.010356	0.0	True	0.000166	0.005018	0.053731	419.230951	0.0	True
lag30	-0.018643	-0.026344	-0.025295	NaN	NaN	False	99.686123	-0.00217	0.005684	NaN	NaN	False	-1079.790411	-0.068419	-0.060915	NaN	NaN	False	0.093789	-0.019627	0.005015	NaN	NaN	False	-110.965932	-0.02355	-0.005915	NaN	NaN	False	-11.564539	-0.062157	-0.004563	NaN	NaN	False	-544.139121	-0.043441	-0.034403	NaN	NaN	False	-11.413114	-0.025079	-0.035468	NaN	NaN	False	-85.992525	-0.016255	-0.002868	NaN	NaN	False	982.396528	-0.024693	0.025078	NaN	NaN	False	0.133749	-0.031523	0.07094	NaN	NaN	False	1.078462	-0.035088	0.030952	NaN	NaN	False	0.000056	0.000361	0.017925	NaN	NaN	False

Auto-correlation/covariance structure

CO(GT); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

PT08.S1(CO); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

NMHC(GT); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

C6H6(GT); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

PT08.S2(NMHC); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

NOx(GT); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

PT08.S3(NOx); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

NO2(GT); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

PT08.S4(NO2); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

PT08.S5(O3); monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

T; monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

RH; monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right) & diff1/diff0(upper/lower)

AH; monthly(top), quarterly(bottom right), yearly(bottom left); correlation/covariance(left/right)

Stationary Analysis

differencing (D=1, d=1, m=24), SARIMAX((0,1,0), (0,1,0,24)) & Standardized GARCH(3,0,3)

	adf				kpss
	stats	pval	number_of_used_lags	adf stationary	stats	pval	number_of_used_lags	kpss stationary
CO(GT)	-24.900195	0.0	27	True	0.067891	0.1	123	True
PT08.S1(CO)	-25.204788	0.0	32	True	0.064395	0.1	112	True
NMHC(GT)	-10.008933	0.0	23	True	0.045934	0.1	45	True
C6H6(GT)	-23.216466	0.0	30	True	0.027501	0.1	85	True
PT08.S2(NMHC)	-23.845618	0.0	33	True	0.032222	0.1	105	True
NOx(GT)	-25.052843	0.0	28	True	0.449359	0.05588	116	True
PT08.S3(NOx)	-25.451232	0.0	34	True	0.051891	0.1	100	True
NO2(GT)	-25.619444	0.0	29	True	0.199061	0.1	109	True
PT08.S4(NO2)	-21.477915	0.0	34	True	0.033935	0.1	88	True
PT08.S5(O3)	-24.778391	0.0	33	True	0.011084	0.1	94	True
T	-22.534557	0.0	37	True	0.044319	0.1	54	True
RH	-26.127431	0.0	31	True	0.007199	0.1	45	True
AH	-29.005741	0.0	25	True	0.003645	0.1	17	True

differencing (D=1, d=1, m=24), SARIMAX((0,1,0), (0,1,0,24))

	adf				kpss
	stats	pval	number_of_used_lags	adf stationary	stats	pval	number_of_used_lags	kpss stationary
CO(GT)	-26.931409	0.0	33	True	0.032225	0.1	196	True
PT08.S1(CO)	-25.612593	0.0	34	True	0.013633	0.1	127	True
NMHC(GT)	-10.750317	0.0	23	True	0.148104	0.1	257	True
C6H6(GT)	-27.828471	0.0	32	True	0.027901	0.1	200	True
PT08.S2(NMHC)	-26.544557	0.0	33	True	0.023625	0.1	150	True
NOx(GT)	-25.496917	0.0	35	True	0.010477	0.1	123	True
PT08.S3(NOx)	-26.476556	0.0	33	True	0.010565	0.1	89	True
NO2(GT)	-24.272786	0.0	36	True	0.025971	0.1	126	True
PT08.S4(NO2)	-26.402711	0.0	33	True	0.02212	0.1	145	True
PT08.S5(O3)	-25.699396	0.0	33	True	0.008484	0.1	108	True
T	-23.662499	0.0	37	True	0.005056	0.1	62	True
RH	-26.636483	0.0	33	True	0.003763	0.1	49	True
AH	-24.410589	0.0	34	True	0.001213	0.1	25	True

	adf				kpss
	stats	pval	number_of_used_lags	adf stationary	stats	pval	number_of_used_lags	kpss stationary
CO(GT)	-10.267951	0.0	37	True	1.326229	0.01	42	False
PT08.S1(CO)	-9.701349	0.0	38	True	0.491353	0.043614	47	False
NMHC(GT)	-2.937991	0.041105	23	True	1.176806	0.01	16	False
C6H6(GT)	-10.300587	0.0	37	True	0.830241	0.01	42	False
PT08.S2(NMHC)	-10.395797	0.0	37	True	1.042781	0.01	43	False
NOx(GT)	-6.883601	0.0	26	True	9.428993	0.01	50	False
PT08.S3(NOx)	-10.581876	0.0	36	True	3.567417	0.01	49	False
NO2(GT)	-7.526296	0.0	32	True	8.06908	0.01	48	False
PT08.S4(NO2)	-5.966929	0.0	37	True	9.684327	0.01	53	False
PT08.S5(O3)	-11.032393	0.0	36	True	1.065825	0.01	48	False
T	-2.883684	0.047278	29	True	7.578053	0.01	55	False
RH	-7.3299	0.0	38	True	3.12812	0.01	52	False
AH	-5.069178	0.000016	25	True	4.324071	0.01	57	False

Exploratory Data Analysis

Exploratory for time series process

Deterministic process exploration of time series features

	CO(GT)			PT08.S1(CO)			NMHC(GT)			C6H6(GT)			PT08.S2(NMHC)			NOx(GT)			PT08.S3(NOx)			NO2(GT)			PT08.S4(NO2)			PT08.S5(O3)			T			RH			AH
	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject	coef	P>\|z\|	reject

const	1.8668	0.000	True	1122.5781	0.000	True	132.3782	0.000	True	8.8940	0.000	True	881.3584	0.000	True	47.5578	0.000	True	978.3144	0.000	True	94.8901	0.000	True	1567.2992	0.000	True	903.3162	0.000	True	16.5477	0.000	True	42.3671	0.000	True	0.7507	0.000	True
trend	5.793e-05	0.001	True	-0.0393	0.000	True	0.1886	0.000	True	0.0010	0.000	True	0.0353	0.000	True	0.0555	0.000	True	-0.0673	0.000	True	-0.0063	0.000	True	0.0290	0.000	True	0.0256	0.000	True	0.0038	0.000	True	0.0006	0.004	True	0.0003	0.000	True
trend_squared	-2.833e-09	0.107	False	4.175e-06	0.000	True	-6.751e-05	0.048	True	-1.24e-07	0.000	True	-4.685e-06	0.000	True	-2.406e-06	0.000	True	4.604e-06	0.000	True	1.361e-06	0.000	True	-1.041e-05	0.000	True	-1.055e-06	0.055	False	-5.67e-07	0.000	True	8.179e-08	0.000	True	-3.241e-08	0.000	True
sin(1,24)	-0.3435	0.000	True	-58.8431	0.000	True	-76.0408	0.000	True	-2.3799	0.000	True	-93.3787	0.000	True	-58.0096	0.000	True	66.7070	0.000	True	-13.9948	0.000	True	-71.3560	0.000	True	-67.4841	0.000	True	-2.6439	0.000	True	7.2555	0.000	True	0.0216	0.000	True
cos(1,24)	0.7431	0.000	True	101.4581	0.000	True	79.3568	0.000	True	3.4164	0.000	True	144.5080	0.000	True	61.1878	0.000	True	-95.3206	0.000	True	26.6262	0.000	True	107.6307	0.000	True	114.2243	0.000	True	3.4038	0.000	True	-8.4095	0.000	True	-0.0074	0.201	False
sin(2,24)	0.5671	0.000	True	89.1333	0.000	True	78.7232	0.000	True	3.0023	0.000	True	116.7752	0.000	True	67.7697	0.000	True	-102.1578	0.000	True	17.1826	0.000	True	111.0971	0.000	True	177.0372	0.000	True	-0.8017	0.000	True	1.7592	0.000	True	0.0140	0.001	True
cos(2,24)	0.2356	0.000	True	33.7553	0.000	True	50.1046	0.000	True	1.4764	0.000	True	42.6933	0.000	True	12.9467	0.000	True	11.4231	0.002	True	1.1648	0.056	False	64.7984	0.000	True	29.0433	0.000	True	-0.4683	0.000	True	2.3813	0.000	True	0.0042	0.465	False
sin(3,24)	-0.0580	0.000	True	-26.0255	0.000	True	-7.6270	0.129	False	-0.7653	0.000	True	-34.5946	0.000	True	-10.6502	0.000	True	36.6993	0.000	True	-2.3773	0.000	True	-31.3248	0.000	True	-31.7965	0.000	True	0.1074	0.188	False	-0.4219	0.026	True	0.0009	0.828	False
cos(3,24)	0.3342	0.000	True	49.4504	0.000	True	39.6495	0.000	True	1.6929	0.000	True	60.9457	0.000	True	32.1642	0.000	True	-20.3776	0.000	True	8.9774	0.000	True	66.9855	0.000	True	77.1826	0.000	True	0.4575	0.000	True	-0.3176	0.218	False	0.0127	0.029	True
s(2,24)	0.2564	0.000	True	40.9947	0.001	True	73.0667	0.003	True	1.5034	0.000	True	52.9256	0.000	True	13.9287	0.181	False	-27.5242	0.041	True	3.9521	0.070	False	57.2217	0.000	True	56.0048	0.014	True	-0.2041	0.608	False	0.8021	0.384	False	0.0072	0.728	False
s(3,24)	0.2972	0.000	True	51.2380	0.000	True	57.6958	0.003	True	1.0449	0.001	True	53.5165	0.000	True	24.3747	0.003	True	-14.6088	0.175	False	6.2627	0.000	True	63.2296	0.000	True	68.5426	0.000	True	0.1012	0.750	False	1.4206	0.054	False	0.0197	0.236	False
s(4,24)	-0.0395	0.413	False	18.8420	0.016	True	-34.9657	0.030	True	-0.7628	0.003	True	1.7356	0.845	False	6.8634	0.320	False	45.7242	0.000	True	3.9174	0.007	True	21.7835	0.043	True	11.4940	0.447	False	0.5425	0.039	True	1.6276	0.008	True	0.0279	0.042	True
s(5,24)	-0.1629	0.001	True	22.6352	0.004	True	-32.6858	0.042	True	-0.6655	0.010	True	1.2761	0.885	False	-18.9986	0.006	True	79.2625	0.000	True	0.5924	0.681	False	36.2809	0.001	True	-0.0954	0.995	False	0.8774	0.001	True	1.6515	0.007	True	0.0342	0.012	True
s(6,24)	0.0659	0.183	False	56.5781	0.000	True	-0.1038	0.995	False	0.3905	0.140	False	38.4212	0.000	True	-9.4056	0.184	False	59.9567	0.000	True	3.3868	0.022	True	74.8513	0.000	True	39.2220	0.012	True	0.8823	0.001	True	2.0498	0.001	True	0.0383	0.007	True
s(7,24)	0.2010	0.000	True	68.1414	0.000	True	6.2004	0.700	False	0.8740	0.001	True	58.0034	0.000	True	7.0059	0.309	False	32.2051	0.000	True	7.0615	0.000	True	86.9150	0.000	True	68.4885	0.000	True	0.6548	0.013	True	2.3737	0.000	True	0.0378	0.006	True
s(8,24)	0.0961	0.043	True	44.9320	0.000	True	3.5582	0.823	False	0.3306	0.191	False	39.2707	0.000	True	0.9803	0.885	False	25.3600	0.004	True	3.8039	0.007	True	63.9781	0.000	True	39.9341	0.007	True	0.3695	0.153	False	2.5238	0.000	True	0.0332	0.014	True
s(9,24)	-0.0388	0.421	False	28.6848	0.000	True	3.3932	0.834	False	-0.0688	0.789	False	19.3427	0.029	True	-7.6752	0.266	False	35.6000	0.000	True	-0.2900	0.841	False	49.0774	0.000	True	16.0293	0.289	False	0.1818	0.490	False	2.6502	0.000	True	0.0301	0.028	True
s(10,24)	-0.0353	0.465	False	29.1878	0.000	True	3.6199	0.824	False	-0.0232	0.928	False	14.9397	0.091	False	-4.2656	0.536	False	53.2641	0.000	True	-0.0069	0.996	False	48.1151	0.000	True	14.9726	0.322	False	0.1829	0.487	False	2.5435	0.000	True	0.0271	0.048	True
s(11,24)	0.0245	0.606	False	28.3382	0.000	True	-8.2052	0.607	False	-0.1370	0.588	False	7.9735	0.359	False	-8.1450	0.230	False	73.5606	0.000	True	-0.6106	0.667	False	43.3273	0.000	True	12.5888	0.397	False	0.3983	0.124	False	2.3685	0.000	True	0.0301	0.025	True
s(12,24)	-0.1061	0.026	True	14.5048	0.060	False	-30.0302	0.061	False	-0.8586	0.001	True	-14.2112	0.104	False	-16.7454	0.014	True	95.6318	0.000	True	-0.9151	0.521	False	21.6749	0.041	True	-8.5199	0.568	False	0.6743	0.009	True	2.1046	0.000	True	0.0347	0.010	True
s(13,24)	-0.1988	0.000	True	10.1817	0.192	False	-48.7850	0.003	True	-1.4119	0.000	True	-15.0520	0.088	False	-24.2334	0.000	True	72.7188	0.000	True	0.1333	0.926	False	10.7292	0.317	False	-14.4253	0.339	False	0.6124	0.020	True	2.6206	0.000	True	0.0351	0.010	True
s(14,24)	0.0958	0.044	True	75.1439	0.000	True	16.6751	0.298	False	1.0258	0.000	True	69.0490	0.000	True	0.8175	0.904	False	11.6361	0.185	False	4.0162	0.005	True	102.0455	0.000	True	63.6718	0.000	True	0.3957	0.128	False	2.9181	0.000	True	0.0331	0.015	True
s(15,24)	0.4543	0.000	True	110.1493	0.000	True	99.8860	0.000	True	3.4901	0.000	True	134.0978	0.000	True	41.4312	0.000	True	-22.1986	0.011	True	9.0113	0.000	True	179.2762	0.000	True	126.9461	0.000	True	0.1641	0.526	False	2.9720	0.000	True	0.0307	0.023	True
s(16,24)	0.2554	0.000	True	44.7241	0.000	True	33.7237	0.038	True	0.7617	0.003	True	41.7777	0.000	True	17.6604	0.010	True	33.2547	0.000	True	4.4187	0.002	True	64.5298	0.000	True	58.8152	0.000	True	0.1058	0.688	False	2.5842	0.000	True	0.0315	0.022	True
s(17,24)	-0.1537	0.001	True	1.6535	0.832	False	-46.0848	0.005	True	-1.5666	0.000	True	-30.0305	0.001	True	-9.2514	0.180	False	77.0868	0.000	True	1.6529	0.252	False	-10.8964	0.311	False	-5.5178	0.715	False	0.8844	0.001	True	0.5469	0.370	False	0.0285	0.038	True
s(18,24)	-0.2001	0.000	True	15.9993	0.037	True	-47.4870	0.003	True	-1.1453	0.000	True	-11.2676	0.195	False	-12.0484	0.075	False	66.7953	0.000	True	2.3077	0.103	False	10.1024	0.339	False	-9.7901	0.510	False	1.2089	0.000	True	0.2972	0.620	False	0.0252	0.061	False
s(19,24)	0.0665	0.168	False	64.8712	0.000	True	8.6532	0.593	False	0.8015	0.002	True	58.5529	0.000	True	0.1879	0.978	False	28.5310	0.001	True	5.6053	0.000	True	88.1275	0.000	True	45.0089	0.003	True	1.2493	0.000	True	0.9491	0.119	False	0.0322	0.019	True
s(20,24)	0.3731	0.000	True	99.6662	0.000	True	62.0683	0.000	True	2.4092	0.000	True	112.3967	0.000	True	19.3744	0.006	True	0.5886	0.949	False	8.7930	0.000	True	147.1244	0.000	True	101.2843	0.000	True	1.0363	0.000	True	1.7462	0.005	True	0.0378	0.007	True
s(21,24)	0.3506	0.000	True	74.9109	0.000	True	41.4635	0.011	True	1.7050	0.000	True	82.3891	0.000	True	22.8307	0.001	True	21.6825	0.015	True	8.2331	0.000	True	113.6375	0.000	True	77.0806	0.000	True	0.7163	0.006	True	1.7301	0.005	True	0.0327	0.017	True
s(22,24)	0.0317	0.512	False	31.0755	0.000	True	9.2083	0.571	False	-0.0420	0.871	False	19.4798	0.028	True	2.7642	0.689	False	45.2817	0.000	True	3.5543	0.014	True	40.9945	0.000	True	22.6438	0.135	False	0.8457	0.001	True	0.6551	0.284	False	0.0243	0.077	False
s(23,24)	-0.2435	0.000	True	-14.6270	0.122	False	-38.4017	0.050	False	-1.8100	0.000	True	-44.3346	0.000	True	-15.6345	0.061	False	57.3659	0.000	True	-1.8344	0.294	False	-37.8063	0.004	True	-45.9646	0.012	True	0.9636	0.002	True	-0.6302	0.394	False	0.0126	0.447	False
s(24,24)	-0.2477	0.001	True	-23.6292	0.045	True	-39.4959	0.106	False	-1.4562	0.000	True	-41.7626	0.002	True	-13.8200	0.185	False	35.5303	0.008	True	-1.9856	0.363	False	-43.7367	0.007	True	-46.8671	0.040	True	0.6421	0.106	False	-0.9811	0.288	False	-0.0007	0.972	False

trend summary

	CO(GT)	PT08.S1(CO)	NMHC(GT)	C6H6(GT)	PT08.S2(NMHC)	NOx(GT)	PT08.S3(NOx)	NO2(GT)	PT08.S4(NO2)	PT08.S5(O3)	T	RH	AH

const	1.866800	1122.5781	132.3782	8.894	881.3584	47.5578	978.3144	94.8901	1567.2992	903.3162	16.5477	42.3671	0.7507
trend	0.000058	-0.0393	0.1886	0.001	0.0353	0.0555	-0.0673	-0.0063	0.0290	0.0256	0.0038	0.0006	0.0003

seasonality summary

	CO(GT)	PT08.S1(CO)	NMHC(GT)	C6H6(GT)	PT08.S2(NMHC)	NOx(GT)	PT08.S3(NOx)	NO2(GT)	PT08.S4(NO2)	PT08.S5(O3)	T	RH	AH
period	s(15,24)	s(15,24)	s(15,24)	s(15,24)	s(15,24)	s(15,24)	s(12,24)	s(15,24)	s(15,24)	s(15,24)	s(19,24)	s(15,24)	s(6,24)
coef	0.4543	110.1493	99.886	3.4901	134.0978	41.4312	95.6318	9.0113	179.2762	126.9461	1.2493	2.972	0.0383

Stochastic process exploration of time series features

			CO(GT)						PT08.S1(CO)						NMHC(GT)						C6H6(GT)						PT08.S2(NMHC)						NOx(GT)						PT08.S3(NOx)						NO2(GT)						PT08.S4(NO2)						PT08.S5(O3)						T						RH						AH
			coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]	coef	std err	z	P>\|z\|	[0.025	0.975]
model name	param symbol	param name
strend	$\\sigma_\\varepsilon^2$	sigma2.irregular	1.458e-09	0.007	2.23e-07	1.000	-0.013	0.013	0.0002	96.132	2.12e-06	1.000	-188.414	188.415	5.3e-14	418.307	1.27e-16	1.000	-819.866	819.866	6.441e-08	0.169	3.8e-07	1.000	-0.332	0.332	3.811e-05	170.628	2.23e-07	1.000	-334.425	334.425	0.0238	55.537	0.000	1.000	-108.826	108.874	0.0006	81.657	7.33e-06	1.000	-160.044	160.045	19.8679	2.528	7.859	0.000	14.913	24.823	1.033e-10	216.925	4.76e-13	1.000	-425.165	425.165	4.344e-06	260.182	1.67e-08	1.000	-509.947	509.947	0.1006	0.010	10.400	0.000	0.082	0.120	0.1959	0.284	0.689	0.491	-0.361	0.753	6.115e-10	1.79e-05	3.42e-05	1.000	-3.5e-05	3.5e-05
	$\\sigma_\\eta^2$	sigma2.trend	4.735e-09	1.67e-09	2.836	0.005	1.46e-09	8.01e-09	0.8443	0.088	9.584	0.000	0.672	1.017	0.0472	0.018	2.634	0.008	0.012	0.082	0.0004	4.77e-05	8.511	0.000	0.000	0.000	0.7082	0.082	8.667	0.000	0.548	0.868	0.2031	0.018	11.182	0.000	0.168	0.239	2.0802	0.168	12.402	0.000	1.751	2.409	0.0135	0.001	10.088	0.000	0.011	0.016	1.4955	0.160	9.370	0.000	1.183	1.808	8.6737	0.740	11.726	0.000	7.224	10.123	0.6361	0.016	39.365	0.000	0.604	0.668	4.2851	0.158	27.163	0.000	3.976	4.594	3.49e-06	2.93e-07	11.909	0.000	2.92e-06	4.06e-06
	$\\sigma_\\kappa^2$	sigma2.cycle	0.4720	0.012	39.577	0.000	0.449	0.495	7089.1688	185.434	38.230	0.000	6725.725	7452.613	1.019e+04	771.010	13.219	0.000	8680.668	1.17e+04	12.2176	0.315	38.824	0.000	11.601	12.834	1.238e+04	326.117	37.950	0.000	1.17e+04	1.3e+04	5502.7222	112.405	48.954	0.000	5282.412	5723.032	7745.2621	173.296	44.694	0.000	7405.608	8084.916	237.3133	5.214	45.517	0.000	227.094	247.532	1.403e+04	410.915	34.135	0.000	1.32e+04	1.48e+04	1.918e+04	527.359	36.366	0.000	1.81e+04	2.02e+04	0.1001	0.016	6.270	0.000	0.069	0.131	6.0336	0.658	9.169	0.000	4.744	7.323	0.0019	4.16e-05	46.691	0.000	0.002	0.002
	$\\lambda_c$	frequency.cycle	0.2701	0.006	46.016	0.000	0.259	0.282	0.3524	0.005	64.570	0.000	0.342	0.363	0.3749	0.020	18.556	0.000	0.335	0.415	0.3503	0.006	57.485	0.000	0.338	0.362	0.3407	0.005	63.952	0.000	0.330	0.351	0.3067	0.004	72.813	0.000	0.298	0.315	0.3436	0.004	85.254	0.000	0.336	0.352	0.3148	0.004	81.049	0.000	0.307	0.322	0.3813	0.007	53.344	0.000	0.367	0.395	0.3891	0.005	73.227	0.000	0.379	0.399	1.0198	0.028	36.986	0.000	0.966	1.074	0.6238	0.041	15.094	0.000	0.543	0.705	0.1898	0.005	36.413	0.000	0.180	0.200
	$\\rho$	damping.cycle	0.8483	0.005	160.053	0.000	0.838	0.859	0.8669	0.004	211.665	0.000	0.859	0.875	0.8110	0.016	51.880	0.000	0.780	0.842	0.8386	0.005	182.079	0.000	0.830	0.848	0.8719	0.004	218.422	0.000	0.864	0.880	0.8665	0.004	236.743	0.000	0.859	0.874	0.8873	0.004	239.450	0.000	0.880	0.895	0.8987	0.003	275.784	0.000	0.892	0.905	0.8324	0.005	172.457	0.000	0.823	0.842	0.8766	0.004	201.633	0.000	0.868	0.885	0.7724	0.022	35.327	0.000	0.730	0.815	0.7079	0.015	46.885	0.000	0.678	0.738	0.9099	0.003	286.604	0.000	0.904	0.916
	$2 \\pi / \\lambda_c$	period.cycle	23.262441	NaN	NaN	NaN	NaN	NaN	17.829697	NaN	NaN	NaN	NaN	NaN	16.75963	NaN	NaN	NaN	NaN	NaN	17.936584	NaN	NaN	NaN	NaN	NaN	18.441988	NaN	NaN	NaN	NaN	NaN	20.486421	NaN	NaN	NaN	NaN	NaN	18.286337	NaN	NaN	NaN	NaN	NaN	19.959293	NaN	NaN	NaN	NaN	NaN	16.478325	NaN	NaN	NaN	NaN	NaN	16.147996	NaN	NaN	NaN	NaN	NaN	6.161194	NaN	NaN	NaN	NaN	NaN	10.072436	NaN	NaN	NaN	NaN	NaN	33.104243	NaN	NaN	NaN	NaN	NaN
lltrend	$\\sigma_\\varepsilon^2$	sigma2.irregular	3.739e-05	0.006	0.007	0.995	-0.011	0.011	0.0195	103.117	0.000	1.000	-202.086	202.126	2.117e-11	424.601	4.99e-14	1.000	-832.204	832.204	1.591e-12	0.173	9.17e-12	1.000	-0.340	0.340	2.965e-07	187.163	1.58e-09	1.000	-366.833	366.833	0.2957	56.284	0.005	0.996	-110.019	110.610	3.518e-05	81.704	4.31e-07	1.000	-160.137	160.137	0.0098	3.276	0.003	0.998	-6.412	6.431	9.3434	219.785	0.043	0.966	-421.427	440.113	8.037e-11	225.024	3.57e-13	1.000	-441.040	441.040	0.0875	0.027	3.236	0.001	0.035	0.141	0.0232	0.304	0.076	0.939	-0.573	0.619	5.637e-12	1.51e-05	3.74e-07	1.000	-2.95e-05	2.95e-05
	$\\sigma_\\zeta^2$	sigma2.level	0.0102	0.001	7.501	0.000	0.008	0.013	476.4186	51.422	9.265	0.000	375.633	577.205	143.4461	62.904	2.280	0.023	20.156	266.736	0.3678	0.049	7.530	0.000	0.272	0.464	530.3651	68.908	7.697	0.000	395.307	665.423	230.8066	22.391	10.308	0.000	186.921	274.692	856.0848	67.441	12.694	0.000	723.903	988.267	8.9299	1.155	7.734	0.000	6.667	11.193	937.4003	88.415	10.602	0.000	764.111	1110.690	9239.9681	562.973	16.413	0.000	8136.561	1.03e+04	0.0914	0.159	0.573	0.567	-0.221	0.404	6.5201	2.599	2.509	0.012	1.426	11.614	0.0014	8.14e-05	17.393	0.000	0.001	0.002
	$\\sigma_\\eta^2$	sigma2.trend	6.767e-13	1.02e-08	6.61e-05	1.000	-2.01e-08	2.01e-08	2.055e-11	0.000	5.57e-08	1.000	-0.001	0.001	1.047e-11	0.003	3.23e-09	1.000	-0.006	0.006	1.282e-13	3.84e-07	3.34e-07	1.000	-7.52e-07	7.52e-07	4.593e-10	0.001	8.83e-07	1.000	-0.001	0.001	2.448e-07	0.000	0.002	0.998	-0.000	0.000	1.792e-08	0.000	4.25e-05	1.000	-0.001	0.001	1.637e-14	4e-06	4.09e-09	1.000	-7.85e-06	7.85e-06	2.869e-05	0.001	0.030	0.976	-0.002	0.002	5.058e-19	0.016	3.19e-17	1.000	-0.031	0.031	0.6094	0.025	24.358	0.000	0.560	0.658	3.8793	0.229	16.926	0.000	3.430	4.329	4.399e-14	3.2e-09	1.38e-05	1.000	-6.26e-09	6.26e-09
	$\\sigma_\\kappa^2$	sigma2.cycle	0.3937	0.011	35.709	0.000	0.372	0.415	6696.9481	219.150	30.559	0.000	6267.421	7126.475	9708.6946	842.320	11.526	0.000	8057.778	1.14e+04	11.6647	0.353	33.037	0.000	10.973	12.357	1.216e+04	388.977	31.271	0.000	1.14e+04	1.29e+04	5165.1579	123.041	41.979	0.000	4924.001	5406.314	6959.5602	196.210	35.470	0.000	6574.996	7344.124	290.6379	7.820	37.167	0.000	275.312	305.964	1.271e+04	463.648	27.421	0.000	1.18e+04	1.36e+04	1.009e+04	532.211	18.957	0.000	9045.861	1.11e+04	0.0846	0.037	2.315	0.021	0.013	0.156	2.0488	1.034	1.981	0.048	0.022	4.076	0.0007	6.85e-05	9.656	0.000	0.001	0.001
	$\\lambda_c$	frequency.cycle	0.3549	0.007	54.377	0.000	0.342	0.368	0.3670	0.007	55.056	0.000	0.354	0.380	0.4027	0.024	16.702	0.000	0.355	0.450	0.3673	0.007	49.527	0.000	0.353	0.382	0.3473	0.006	54.072	0.000	0.335	0.360	0.3254	0.005	65.489	0.000	0.316	0.335	0.3589	0.005	74.021	0.000	0.349	0.368	0.3047	0.005	57.097	0.000	0.294	0.315	0.4124	0.009	46.494	0.000	0.395	0.430	0.5102	0.006	81.920	0.000	0.498	0.522	1.0259	0.039	26.588	0.000	0.950	1.102	0.8665	0.069	12.477	0.000	0.730	1.003	0.2907	0.007	40.772	0.000	0.277	0.305
	$\\rho$	damping.cycle	0.8464	0.005	173.103	0.000	0.837	0.856	0.8637	0.004	194.453	0.000	0.855	0.872	0.8109	0.016	51.546	0.000	0.780	0.842	0.8382	0.005	177.924	0.000	0.829	0.847	0.8692	0.004	202.716	0.000	0.861	0.878	0.8654	0.004	230.590	0.000	0.858	0.873	0.8891	0.004	226.822	0.000	0.881	0.897	0.8834	0.004	225.678	0.000	0.876	0.891	0.8314	0.005	161.369	0.000	0.821	0.842	0.8922	0.005	169.447	0.000	0.882	0.903	0.7890	0.038	20.866	0.000	0.715	0.863	0.7217	0.043	16.811	0.000	0.638	0.806	0.9246	0.005	173.539	0.000	0.914	0.935
	$2 \\pi / \\lambda_c$	period.cycle	17.704101	NaN	NaN	NaN	NaN	NaN	17.120396	NaN	NaN	NaN	NaN	NaN	15.602645	NaN	NaN	NaN	NaN	NaN	17.106412	NaN	NaN	NaN	NaN	NaN	18.091521	NaN	NaN	NaN	NaN	NaN	19.309113	NaN	NaN	NaN	NaN	NaN	17.506785	NaN	NaN	NaN	NaN	NaN	20.62089	NaN	NaN	NaN	NaN	NaN	15.235658	NaN	NaN	NaN	NaN	NaN	12.315142	NaN	NaN	NaN	NaN	NaN	6.124559	NaN	NaN	NaN	NaN	NaN	7.251224	NaN	NaN	NaN	NaN	NaN	21.613985	NaN	NaN	NaN	NaN	NaN

Descriptive Statistics

Cycle subseries description

Monthly description

monthly aggregation about volatility(;standard error) and mean

cross-sectional description

	Date	2004-03	2004-04	2004-05	2004-06	2004-07	2004-08	2004-09	2004-10	2004-11	2004-12	2005-01	2005-02	2005-03	2005-04
CO(GT)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	0.3000	0.3000	0.1000	0.1000	0.1000	0.1000	0.2000	0.4000	0.1000	0.2000	0.1000	0.3000	0.1000	0.3000
	max	8.1000	7.3000	6.5000	6.4000	5.3000	3.5000	7.5000	9.5000	11.9000	9.9000	8.7000	8.4000	7.5000	5.0000
	mean	2.2483	2.2404	1.8668	1.8688	1.7521	1.2496	2.1084	2.6144	2.6496	2.7188	2.0857	2.0822	2.0136	1.1936
	std	1.3503	1.2551	1.1217	1.1032	0.9886	0.4999	1.3109	1.3611	1.8917	1.6800	1.3695	1.3120	1.3764	0.8170
PT08.S1(CO)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	818.0000	753.0000	736.0000	708.0000	723.0000	711.0000	718.0000	704.0000	647.0000	691.0000	744.0000	755.0000	715.0000	811.0000
	max	2040.0000	1875.0000	1763.0000	1506.0000	1626.0000	1393.0000	1728.0000	1908.0000	2008.0000	1881.0000	1835.0000	1846.0000	1818.0000	1446.0000
	mean	1222.8196	1161.7003	1075.4309	1019.2030	1046.3647	979.5625	1079.9986	1184.9679	1132.1486	1084.4706	1109.0407	1083.8458	1145.3640	953.7126
	std	241.0385	228.0895	194.4596	159.0491	158.3249	117.1149	198.3246	242.9786	273.0584	213.1563	215.5116	185.2794	197.1283	125.4414
NMHC(GT)	count	510.0000	720.0000	1.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
	min	7.0000	9.0000	275.0000	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	max	797.0000	1189.0000	275.0000	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	mean	170.5805	252.4566	275.0000	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	std	141.6348	202.9348	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
C6H6(GT)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	0.6000	0.5000	0.5000	0.5000	1.3000	1.0000	0.9000	0.5000	0.2000	0.4000	0.1000	0.2000	0.2000	0.8000
	max	39.2000	40.3000	40.2000	36.9000	37.3000	30.7000	41.2000	52.1000	63.7000	50.8000	43.0000	33.9000	35.5000	22.4000
	mean	9.9327	10.3847	10.1865	10.5798	10.5968	6.9949	11.5172	13.5276	12.5118	9.5040	9.0246	7.4913	8.7322	4.2851
	std	7.0605	7.4249	6.6894	6.4530	6.2274	3.7573	7.9367	9.1119	9.8386	7.0804	6.9725	5.4261	6.6770	3.7984
PT08.S2(NMHC)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	457.0000	448.0000	437.0000	437.0000	527.0000	494.0000	486.0000	444.0000	397.0000	426.0000	383.0000	402.0000	387.0000	473.0000
	max	1754.0000	1776.0000	1776.0000	1705.0000	1713.0000	1567.0000	1795.0000	2007.0000	2214.0000	1983.0000	1831.0000	1639.0000	1675.0000	1362.0000
	mean	935.6431	948.4665	949.4093	964.9694	971.3774	837.5784	991.7029	1058.5105	1011.2014	913.4517	890.5241	839.7649	887.9157	698.7356
	std	258.9974	269.3944	243.8496	237.7542	224.4253	155.9563	272.4993	294.2151	327.3430	257.8404	268.6751	218.1439	253.3175	173.3043
NOx(GT)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	12.0000	10.0000	4.0000	9.0000	10.0000	2.0000	19.0000	33.0000	13.0000	31.0000	17.0000	25.0000	29.0000	30.0000
	max	478.0000	378.0000	383.0000	441.0000	427.0000	282.0000	891.0000	952.0000	1389.0000	1479.0000	1230.0000	1227.0000	959.0000	594.0000
	mean	139.7090	134.7195	118.1636	118.2016	123.3433	73.3715	267.1590	322.0476	412.2313	405.8573	341.4330	307.9954	306.8580	175.5747
	std	82.8739	70.7231	65.1873	77.7787	81.1308	40.6644	149.5296	154.6412	284.8950	248.9821	232.9381	207.1190	188.4357	109.4848
PT08.S3(NOx)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	537.0000	461.0000	452.0000	459.0000	410.0000	416.0000	388.0000	325.0000	322.0000	334.0000	355.0000	383.0000	330.0000	415.0000
	max	1935.0000	1923.0000	1904.0000	1941.0000	1274.0000	1398.0000	1531.0000	1590.0000	2121.0000	2683.0000	1881.0000	1665.0000	1804.0000	1257.0000
	mean	1029.1725	934.3643	947.8272	898.8842	804.8553	833.6421	810.5808	688.0169	789.8806	878.6447	789.3091	788.2502	709.2681	899.4713
	std	268.1309	253.0501	233.0840	214.4089	163.6861	155.5296	211.5278	203.7557	315.4736	331.5311	258.1564	203.3980	216.4239	172.8037
NO2(GT)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	20.0000	17.0000	8.0000	16.0000	17.0000	5.0000	2.0000	29.0000	13.0000	27.0000	17.0000	25.0000	27.0000	29.0000
	max	194.0000	196.0000	179.0000	226.0000	233.0000	185.0000	225.0000	194.0000	288.0000	269.0000	285.0000	340.0000	248.0000	190.0000
	mean	100.8606	93.9107	90.7028	92.1076	102.1456	67.8495	103.4455	86.2438	119.9897	122.1628	132.6206	158.1743	136.3770	108.9310
	std	32.5799	29.2103	30.2780	38.7665	40.3100	24.8443	40.9144	27.3533	53.8030	40.3027	46.1709	57.9836	45.5583	40.4730
PT08.S4(NO2)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	1050.0000	955.0000	1048.0000	1227.0000	1234.0000	1084.0000	1059.0000	1050.0000	697.0000	682.0000	657.0000	621.0000	551.0000	742.0000
	max	2679.0000	2684.0000	2667.0000	2746.0000	2662.0000	2404.0000	2555.0000	2775.0000	2643.0000	2405.0000	2083.0000	1870.0000	2147.0000	1777.0000
	mean	1572.0725	1609.0432	1599.5351	1719.4459	1643.7175	1577.9504	1544.7438	1636.9817	1372.2347	1213.9987	1151.4542	1053.9850	1225.3955	976.4598
	std	280.5254	287.1709	261.0709	244.9339	226.3288	181.8614	286.1289	302.1502	355.8909	263.3822	271.0564	207.4259	275.9075	169.7447
PT08.S5(O3)	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	341.0000	263.0000	301.0000	334.0000	386.0000	368.0000	342.0000	392.0000	261.0000	318.0000	253.0000	252.0000	221.0000	322.0000
	max	2359.0000	2108.0000	2054.0000	2202.0000	2475.0000	1607.0000	2321.0000	2372.0000	2522.0000	2523.0000	2331.0000	2494.0000	2159.0000	1729.0000
	mean	1027.4941	1002.7288	927.2517	935.6565	994.4457	775.6035	1034.3404	1163.9053	1171.3542	1080.6730	1096.5487	1028.9280	1083.8291	646.8506
	std	381.6004	376.9071	324.1343	306.4241	352.3788	221.8787	355.5132	377.5972	469.6605	413.4739	445.1649	416.3604	408.9590	305.9041
T	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	6.1000	7.4000	7.4000	16.5000	16.2000	18.6000	11.9000	12.6000	1.3000	1.2000	1.0000	0.3000	-1.9000	8.9000
	max	29.3000	31.3000	32.8000	42.2000	44.6000	40.5000	40.7000	30.8000	26.8000	20.3000	16.9000	19.9000	28.8000	30.0000
	mean	14.3908	16.8004	20.2230	26.4517	29.4131	29.1182	24.5979	20.5012	13.4854	11.1088	8.2079	7.0960	13.2206	16.6609
	std	4.4475	4.7505	5.1867	5.8866	6.1716	5.1330	5.4366	3.5880	4.9904	3.4512	3.7218	3.3541	6.3927	5.4252
RH	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	14.9000	16.2000	9.2000	11.9000	9.6000	10.0000	13.8000	31.8000	14.0000	16.3000	17.2000	18.0000	13.5000	9.9000
	max	83.2000	82.4000	85.2000	82.3000	69.3000	81.8000	87.2000	86.5000	87.1000	88.7000	86.6000	86.6000	84.0000	63.1000
	mean	50.1708	50.5945	43.6366	39.7443	33.0613	42.7673	43.9763	61.8939	59.2749	57.6148	56.4503	51.8323	50.8980	35.4828
	std	14.2653	15.9084	16.6971	13.9907	12.7009	14.4153	15.0220	11.2454	16.0088	16.4268	13.8457	16.4541	16.6005	13.1440
AH	count	510.0000	720.0000	744.0000	720.0000	744.0000	744.0000	720.0000	744.0000	720.0000	744.0000	744.0000	672.0000	744.0000	87.0000
	min	0.4023	0.4868	0.3754	0.7502	0.7158	0.6591	0.6514	0.9107	0.1988	0.2749	0.2477	0.2269	0.1847	0.3866
	max	1.0945	1.4852	1.6296	1.9390	2.0042	2.1806	2.2310	2.0224	1.9800	1.3713	1.0567	1.0859	1.3930	0.8642
	mean	0.7894	0.9196	0.9572	1.2733	1.2427	1.6153	1.2846	1.4640	0.9400	0.7780	0.6341	0.5153	0.7817	0.6216
	std	0.1399	0.1699	0.1985	0.1995	0.2434	0.2862	0.2919	0.2195	0.3603	0.2741	0.2185	0.1405	0.2916	0.1164

longitudinal description

	Autocorrelation												Heteroskedasticity												Normality												Stationary
	2004-03	2004-04	2004-05	2004-06	2004-07	2004-08	2004-09	2004-10	2004-11	2004-12	2005-01	2005-02	2004-03	2004-04	2004-05	2004-06	2004-07	2004-08	2004-09	2004-10	2004-11	2004-12	2005-01	2005-02	2004-03	2004-04	2004-05	2004-06	2004-07	2004-08	2004-09	2004-10	2004-11	2004-12	2005-01	2005-02	2004-03	2004-04	2004-05	2004-06	2004-07	2004-08	2004-09	2004-10	2004-11	2004-12	2005-01	2005-02
CO(GT)	True	True	True	True	True	True	True	True	True	True	True	True	False	False	True	False	True	False	True	True	True	True	True	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	True	True	True	True	True	True	True	False	True
PT08.S1(CO)	True	True	True	True	True	True	True	True	True	True	True	True	False	False	False	False	False	False	False	False	False	False	True	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	True	True	True	False	False	False	False	False	False	False
C6H6(GT)	True	True	True	True	True	True	True	True	True	True	True	True	False	False	False	False	False	False	True	False	False	True	True	True	False	False	False	False	False	False	False	False	False	False	False	False	False	False	True	True	True	False	True	True	True	False	False	False
PT08.S2(NMHC)	True	True	True	True	True	True	True	True	True	True	True	True	False	False	False	False	False	False	False	False	False	False	True	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	True	True	True	False	True	True	False	False	False	True
NOx(GT)	True	True	True	True	True	True	True	True	True	True	True	True	True	True	True	False	True	False	True	True	True	False	True	True	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	True	False	True	True	True	False	False	False	False
PT08.S3(NOx)	True	True	True	True	True	True	True	True	True	True	True	True	True	False	False	False	False	False	False	False	False	True	True	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	True	False	False	False	False	True	False	False
NO2(GT)	True	True	True	True	True	True	True	True	True	True	True	True	True	False	False	False	False	False	False	True	True	True	False	False	False	False	True	False	False	False	False	False	False	False	True	False	False	False	True	False	False	True	False	False	False	False	True	False
PT08.S4(NO2)	True	True	True	True	True	True	True	True	True	True	True	True	True	False	False	False	False	False	False	False	False	True	True	False	False	True	False	False	False	False	False	False	False	False	False	False	False	False	False	True	True	False	False	False	False	False	False	False
PT08.S5(O3)	True	True	True	True	True	True	True	True	True	True	True	True	False	False	False	False	False	False	False	False	True	False	True	True	False	False	False	False	False	False	False	False	False	False	False	False	False	False	True	True	True	True	False	False	False	False	False	False
T	True	True	True	True	True	True	True	True	True	True	True	True	True	False	True	True	False	False	True	False	True	True	True	True	True	False	False	False	False	False	False	False	False	True	False	False	False	False	False	False	False	False	False	False	False	False	False	False
RH	True	True	True	True	True	True	True	True	True	True	True	True	False	True	True	True	False	True	True	True	False	True	True	True	False	False	False	False	False	False	False	False	False	False	False	False	True	False	False	False	False	False	False	False	False	False	False	False
AH	True	True	True	True	True	True	True	True	True	True	True	True	True	False	True	False	False	True	False	False	True	True	True	True	True	True	False	True	False	False	False	False	False	False	False	False	False	True	False	True	False	False	True	True	False	False	False	False
NMHC(GT)	True	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	False	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	False	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	True	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN

Weekly description

weekly volatility(;standard error) and mean

cross-sectional description

	Date	2004-03-14	2004-03-21	2004-03-28	2004-04-04	2004-04-11	2004-04-18	2004-04-25	2004-05-02	2004-05-09	2004-05-16	2004-05-23	2004-05-30	2004-06-06	2004-06-13	2004-06-20	2004-06-27	2004-07-04	2004-07-11	2004-07-18	2004-07-25	2004-08-01	2004-08-08	2004-08-15	2004-08-22	2004-08-29	2004-09-05	2004-09-12	2004-09-19	2004-09-26	2004-10-03	2004-10-10	2004-10-17	2004-10-24	2004-10-31	2004-11-07	2004-11-14	2004-11-21	2004-11-28	2004-12-05	2004-12-12	2004-12-19	2004-12-26	2005-01-02	2005-01-09	2005-01-16	2005-01-23	2005-01-30	2005-02-06	2005-02-13	2005-02-20	2005-02-27	2005-03-06	2005-03-13	2005-03-20	2005-03-27	2005-04-03	2005-04-10
CO(GT)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	0.6000	0.5000	0.3000	0.5000	0.3000	0.3000	0.3000	0.3000	0.4000	0.2000	0.2000	0.1000	0.1000	0.3000	0.3000	0.2000	0.3000	0.2000	0.1000	0.1000	0.4000	0.1000	0.4000	0.3000	0.4000	0.5000	0.2000	0.3000	0.3000	0.4000	0.7000	0.4000	0.7000	0.4000	0.4000	0.2000	0.1000	0.1000	0.6000	0.3000	0.6000	0.2000	0.4000	0.5000	0.4000	0.1000	0.1000	0.3000	0.4000	0.3000	0.4000	0.2000	0.1000	0.1000	0.1000	0.3000	0.4000
	max	6.9000	8.1000	5.2000	6.2000	6.3000	7.3000	5.6000	7.2000	5.4000	6.3000	6.5000	4.0000	4.8000	6.4000	5.0000	5.0000	5.7000	5.3000	5.0000	4.4000	3.4000	3.0000	2.9000	2.5000	3.5000	5.8000	5.4000	6.7000	7.3000	7.5000	7.0000	4.8000	8.4000	9.5000	9.2000	6.8000	10.2000	11.9000	9.4000	6.3000	9.9000	9.1000	4.7000	5.9000	5.9000	8.7000	3.0000	6.8000	8.4000	5.6000	6.3000	6.1000	6.0000	7.4000	7.5000	5.1000	5.0000
	mean	2.4506	2.6537	1.8927	2.1650	2.0068	2.3141	2.1462	2.2720	2.0241	2.1638	1.9963	1.3697	1.6205	1.9865	1.7730	1.8568	1.9047	1.8246	1.8738	1.6795	1.5913	1.2884	1.1648	1.2025	1.3420	1.7837	1.9728	1.9478	2.2826	2.5729	2.4509	2.4985	2.7158	2.7852	2.7045	1.9112	2.5132	3.4701	2.7870	2.0686	3.1863	3.0270	2.3226	2.3946	2.5722	2.2430	1.0632	2.2738	2.5226	1.7012	2.0538	1.7202	1.7614	2.2780	2.2935	1.4516	1.9848
	std	1.3316	1.6240	0.9951	1.1587	1.1074	1.4008	1.0486	1.3669	1.0485	1.2524	1.2566	0.7866	0.8287	1.3338	1.0076	1.0246	1.1261	1.2067	1.1663	0.8714	0.6105	0.5345	0.5129	0.3892	0.5119	1.0108	0.9894	1.1139	1.5753	1.4534	1.1765	1.0516	1.4513	1.7545	1.8198	1.3615	1.8546	2.1823	1.7779	1.0741	1.9423	1.9507	0.9234	1.2384	1.3097	1.6201	0.5877	1.5138	1.5621	0.9233	1.1288	1.1677	1.3583	1.4975	1.4849	0.9246	1.4878
PT08.S1(CO)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	831.0000	869.0000	834.0000	818.0000	797.0000	753.0000	763.0000	767.0000	743.0000	787.0000	771.0000	738.0000	729.0000	726.0000	708.0000	719.0000	809.0000	775.0000	723.0000	834.0000	742.0000	788.0000	738.0000	711.0000	749.0000	784.0000	806.0000	752.0000	718.0000	741.0000	820.0000	704.0000	760.0000	791.0000	752.0000	647.0000	667.0000	814.0000	797.0000	709.0000	699.0000	691.0000	744.0000	862.0000	819.0000	795.0000	744.0000	787.0000	844.0000	802.0000	844.0000	715.0000	841.0000	911.0000	878.0000	811.0000	864.0000
	max	1898.0000	2040.0000	1597.0000	1722.0000	1757.0000	1875.0000	1747.0000	1771.0000	1597.0000	1754.0000	1763.0000	1485.0000	1501.0000	1496.0000	1440.0000	1332.0000	1529.0000	1611.0000	1339.0000	1626.0000	1380.0000	1381.0000	1268.0000	1175.0000	1314.0000	1488.0000	1506.0000	1571.0000	1600.0000	1728.0000	1840.0000	1464.0000	1884.0000	1908.0000	1915.0000	1578.0000	1802.0000	2008.0000	1816.0000	1604.0000	1881.0000	1739.0000	1472.0000	1741.0000	1526.0000	1835.0000	1198.6590	1713.0000	1846.0000	1464.0000	1527.0000	1567.0000	1573.0000	1710.0000	1818.0000	1531.0000	1446.0000
	mean	1305.1176	1336.1369	1103.5774	1199.0624	1116.2187	1139.5357	1142.7857	1168.7381	1058.7381	1122.3155	1154.8452	975.2656	984.5714	1027.4702	1002.6683	1008.7851	1084.8274	1060.1131	1000.8333	1118.4762	997.1924	1025.6429	973.1601	937.7024	957.0334	1059.4762	1078.7620	1079.4881	1076.9167	1160.8818	1258.4048	1000.2321	1274.0357	1193.4405	1188.2500	970.2202	1045.9583	1315.3155	1170.6369	1041.0536	1099.0182	1126.2505	1013.8838	1165.2902	1205.6488	1165.3393	904.3871	1109.8631	1147.0618	1046.5119	1067.7024	1003.2619	1117.3204	1204.7976	1243.6786	1018.9643	1090.5333
	std	218.3815	259.8206	160.3252	209.4062	195.4378	226.5464	239.8161	238.4217	179.8965	206.6689	204.6472	148.7877	150.7783	175.5138	138.3322	138.5456	161.8965	184.4432	128.1401	165.2033	120.4266	123.8964	113.4518	99.5979	97.0059	151.2495	152.0301	200.5149	232.9801	225.1351	237.1526	165.1213	242.0687	238.7695	269.0931	197.0507	242.8034	262.4005	228.1977	168.8166	192.2486	252.5993	148.7457	174.6899	198.3606	238.9035	100.4423	201.6630	224.9558	123.3061	149.9145	186.6587	173.2835	180.8384	200.6301	151.1370	192.3185
NMHC(GT)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	121.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
	min	7.0000	11.0000	19.0000	18.0000	30.0000	9.0000	20.0000	17.0000	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	max	488.0000	685.0000	797.0000	1042.0000	1084.0000	1189.0000	899.0000	1129.0000	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	mean	127.4811	185.7475	170.7941	250.8988	215.0660	260.3191	248.4291	267.6529	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
	std	101.5640	128.1449	145.6729	205.3381	190.0289	215.2524	178.4855	224.4483	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN	NaN
C6H6(GT)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	1.0000	1.3000	0.6000	0.8000	0.7000	0.5000	0.7000	0.6000	1.0000	1.0000	1.2000	0.5000	1.1000	1.2000	0.5000	1.2000	2.6000	2.2000	1.4000	1.3000	1.8000	1.6000	1.5000	1.0000	1.7000	1.7000	1.0000	1.2000	0.9000	1.9000	2.5000	0.5000	1.6000	1.2000	1.2000	0.2000	0.4000	1.5000	1.2000	0.5000	1.8000	0.5000	0.4000	1.4000	1.3000	0.7000	0.1000	0.3000	0.6000	0.5000	0.5000	0.2000	0.5000	1.1000	1.2000	0.8000	0.8000
	max	32.6000	39.2000	24.6000	31.9000	33.7000	33.7000	40.3000	36.2000	26.5000	37.4000	38.9000	40.2000	27.9000	36.9000	30.2000	30.2000	33.5000	31.0000	30.4000	37.3000	26.7000	26.0000	18.7000	16.0000	21.0000	35.2000	34.5000	35.9000	41.2000	39.3000	44.7000	25.6000	43.7000	52.1000	48.2000	32.3000	47.7000	63.7000	43.9000	26.4000	50.8000	36.3000	23.4000	25.3000	28.4000	43.0000	13.5298	32.4000	26.8000	33.9000	27.9000	28.0000	27.0000	33.5000	35.5000	26.3000	22.4000
	mean	10.0647	12.6423	8.1214	9.4592	8.8895	8.9256	11.5554	11.2310	9.2524	11.7476	11.0226	9.2386	9.1494	11.5696	10.3668	10.0806	11.2304	11.2768	10.6315	11.1583	9.2114	8.2232	6.2918	5.7815	6.7784	10.9036	10.1461	11.1196	12.0655	13.1793	14.8548	8.6893	16.6601	14.7214	14.8494	8.1185	10.5929	16.8435	11.8804	8.6220	10.9322	9.9802	5.8564	9.3620	11.9423	11.3595	3.7707	9.2732	8.3489	6.5500	6.9833	6.1190	8.2978	9.9107	10.5446	5.6411	8.4400
	std	6.3279	8.5044	5.3163	6.2826	5.9616	6.8694	8.6339	7.4288	5.8697	7.6093	7.0110	6.4681	5.4588	7.7917	5.8662	5.6852	6.2450	6.9584	6.2690	6.8935	4.9555	4.2751	3.1604	2.5729	2.8600	6.9386	6.0470	7.3427	9.1214	8.6285	9.7035	5.9828	9.2601	9.8026	10.6848	6.8635	8.0060	11.1612	8.9023	5.3818	7.3049	7.0345	3.7798	5.2468	6.9954	8.5056	3.0201	7.3093	4.8841	4.6467	4.8940	5.1732	6.2447	7.1828	7.5829	4.6747	6.8651
PT08.S2(NMHC)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	501.0000	525.0000	457.0000	477.0000	464.0000	448.0000	471.0000	454.0000	502.0000	501.0000	521.0000	437.0000	505.0000	520.0000	437.0000	522.0000	624.0000	602.0000	540.0000	527.0000	569.0000	553.0000	544.0000	494.0000	559.0000	565.0000	501.0000	521.0000	486.0000	577.0000	620.0000	444.0000	555.0000	519.0000	516.0000	397.0000	426.0000	548.0000	518.0000	437.0000	567.0000	437.0000	426.0000	540.0000	532.0000	470.0000	383.0000	415.0000	453.0000	437.0000	440.0000	387.0000	443.0000	508.0000	517.0000	473.0000	478.0000
	max	1610.0000	1754.0000	1418.0000	1595.0000	1636.0000	1637.0000	1776.0000	1690.0000	1466.0000	1716.0000	1748.0000	1776.0000	1501.0000	1705.0000	1556.0000	1556.0000	1631.0000	1575.0000	1561.0000	1713.0000	1472.0000	1454.0000	1259.0000	1181.0000	1325.0000	1669.0000	1654.0000	1684.0000	1795.0000	1756.0000	1866.0000	1444.0000	1846.0000	2007.0000	1935.0000	1605.0000	1924.0000	2214.0000	1851.0000	1465.0000	1983.0000	1692.0000	1389.0000	1438.0000	1512.0000	1831.0000	1044.2834	1605.0000	1474.0000	1639.0000	1502.0000	1502.0000	1479.0000	1632.0000	1675.0000	1461.0000	1362.0000
	mean	947.0784	1030.4405	872.2619	921.8828	895.9199	893.6488	984.6190	984.6488	917.2976	1004.4524	980.1964	909.7589	917.7917	992.3512	953.8116	953.6227	996.2976	991.0714	972.6786	986.5238	926.0643	889.0774	809.8535	789.8274	828.0534	978.2083	950.0481	983.6726	1000.3869	1049.8262	1101.2619	891.8512	1165.1012	1096.7262	1092.1190	850.7381	950.8810	1159.6071	998.6190	893.7440	957.8152	933.9233	780.2711	913.4105	1013.5357	977.7976	666.0265	905.8929	867.2024	808.6548	824.8929	776.1607	873.2757	933.7202	957.6131	762.9702	862.2667
	std	238.5672	284.4188	220.0662	238.9947	227.1439	262.0269	302.1259	263.2765	228.5458	261.8931	252.3311	240.0438	211.7219	279.1132	225.1439	214.4003	220.4933	247.2923	225.4909	247.1389	188.4348	172.6679	140.3554	122.0652	124.9944	243.8394	221.6805	254.0970	312.2914	282.3680	303.8823	235.3236	282.4253	303.9625	332.5951	281.1881	291.5608	325.3868	297.9177	219.2484	247.3834	264.5793	173.1016	205.0003	253.5595	300.2219	162.8270	269.1022	199.5360	195.6405	208.5739	228.9093	241.1039	262.4726	266.7845	200.0170	295.2310
NOx(GT)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	16.0000	18.0000	12.0000	15.0000	12.0000	16.0000	14.0000	10.0000	14.0000	21.0000	14.0000	13.0000	4.0000	19.0000	9.0000	15.0000	24.0000	10.0000	13.0000	10.0000	14.0000	2.0000	6.0000	11.0000	12.0000	35.8227	49.0000	32.0000	19.0000	60.0000	50.0000	33.0000	94.0000	43.0000	44.0000	13.0000	24.0000	60.0000	47.0000	31.0000	83.0000	41.0000	50.0000	54.0000	64.0000	41.0000	17.0000	39.0000	51.0000	28.0000	38.0000	25.0000	35.0000	68.0000	73.0000	30.0000	52.0000
	max	383.0000	478.0000	275.0000	378.0000	329.0000	352.0000	358.0000	368.0000	320.0000	383.0000	346.0000	289.0000	248.0000	441.0000	311.0000	387.0000	350.0000	392.0000	427.0000	395.0000	297.0000	282.0000	188.0000	190.0000	216.0000	487.0000	631.0000	891.0000	803.0000	799.0000	693.0000	565.0000	895.0000	952.0000	1052.0000	1247.0000	1290.0000	1389.0000	1184.0000	968.0000	1479.0000	1220.0000	832.0000	1130.0000	910.0000	1230.0000	378.5265	1017.0000	1227.0000	854.0000	757.0000	959.0000	900.0000	841.0000	874.0000	673.0000	594.0000
	mean	156.1910	166.6443	113.6746	130.2265	124.9728	143.2190	126.2778	129.7824	122.7057	136.1644	120.0673	100.1096	102.7416	134.0854	104.5188	119.8590	123.6311	139.3356	139.0624	116.7468	96.2353	85.5326	58.0815	68.3541	78.7968	210.4062	270.7143	253.8619	253.6453	321.3780	291.0993	308.7129	321.3980	366.8319	343.1987	314.3488	405.8784	600.5922	420.3260	307.5024	529.7898	386.1041	345.0517	360.6073	413.0174	425.1157	167.2208	372.9418	359.9968	253.9934	279.6451	268.5826	327.5737	333.3690	316.2500	203.3631	263.3333
	std	83.4045	96.9249	59.4526	66.8091	67.5853	77.7920	60.1739	75.7332	65.1637	76.0178	68.0286	45.4698	60.9845	93.2354	64.6795	76.9657	76.7388	94.7213	89.7805	78.1290	57.0237	50.4362	30.4865	28.9763	38.4405	116.1754	122.5449	139.2661	179.9484	163.2265	128.0536	118.0611	148.1454	210.9215	214.6588	218.4351	268.4513	335.1495	273.6473	155.1489	321.5270	231.8067	142.5871	206.4254	208.7022	294.9770	85.6651	248.6809	253.7047	145.1205	148.4989	181.6178	203.0508	192.4670	184.0123	122.4991	199.5061
PT08.S3(NOx)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	624.0000	537.0000	652.0000	539.0000	494.0000	482.0000	478.0000	461.0000	518.0000	452.0000	484.0000	632.0000	588.0000	507.0000	517.0000	523.0000	459.0000	472.0000	498.0000	410.0000	470.0000	455.0000	519.0000	580.0000	499.0000	388.0000	529.0000	469.0000	425.0000	411.0000	360.0000	475.0000	348.0000	325.0000	328.0000	429.0000	356.0000	322.0000	341.0000	466.0000	334.0000	402.0000	443.0000	416.0000	414.0000	355.0000	629.0677	383.0000	389.0000	457.0000	411.0000	399.0000	407.0000	346.0000	330.0000	370.0000	415.0000
	max	1918.0000	1620.0000	1935.0000	1699.0000	1826.0000	1923.0000	1783.0000	1826.0000	1635.0000	1554.0000	1566.0000	1904.0000	1570.0000	1534.0000	1941.0000	1385.0000	1185.0000	1254.0000	1274.0000	1242.0000	1204.0000	1203.0000	1281.0000	1398.0000	1189.0000	1327.0000	1370.0000	1472.0000	1531.0000	1221.0000	1081.0000	1590.0000	1226.0000	1291.0000	1370.0000	2121.0000	1775.0000	1207.0000	2095.0000	2683.0000	1731.0000	1726.0000	1568.0000	1110.0000	1144.0000	1315.0000	1881.0000	1486.0000	1378.0000	1491.0000	1349.0000	1804.0000	1490.0000	1049.0000	1069.0000	1257.0000	1116.0000
	mean	1097.7549	924.8929	1071.5417	964.7617	977.9307	970.8631	927.8036	892.0595	932.1964	869.9405	883.5714	1104.9490	993.5298	913.8452	900.6559	863.8894	792.2500	815.7321	826.6786	762.3869	812.6865	783.5417	864.4610	895.6429	822.1624	728.7679	866.1735	828.2321	822.2560	718.4379	644.4345	852.8333	603.1726	656.8512	678.6369	967.8452	849.7560	632.5000	918.7857	944.5357	823.9854	813.6136	871.9893	709.1816	659.6071	732.9167	1048.1742	766.4583	734.9950	810.7381	796.8929	908.1310	737.1814	645.6429	608.3750	805.2143	745.2667
	std	294.0592	220.5527	262.7886	236.6762	237.8954	280.3216	262.1432	235.2968	233.1504	218.4521	209.6953	221.2966	197.8279	229.0454	232.6463	169.5926	156.1162	178.2363	155.5282	176.7005	142.7198	147.0559	158.1316	151.6203	123.8031	180.7948	161.4553	203.4579	256.5547	184.3731	170.1049	224.0442	161.0118	186.0237	229.8328	394.9105	290.9927	189.2264	419.2740	413.1304	217.8770	270.5445	194.3199	160.1870	189.8977	230.1775	261.2644	213.6051	184.3915	175.1869	201.3900	291.2265	195.7779	162.1011	153.8856	192.7991	232.1337
NO2(GT)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	28.0000	28.0000	20.0000	26.0000	19.0000	25.0000	20.0000	17.0000	22.0000	25.0000	23.0000	19.0000	8.0000	30.0000	16.0000	24.0000	39.0000	19.0000	22.0000	17.0000	21.0000	5.0000	5.0000	12.0000	21.0000	27.0000	41.0000	23.0000	2.0000	45.0000	38.0000	29.0000	42.0000	30.0000	26.0000	13.0000	21.0000	44.0000	38.0000	27.0000	61.0000	37.0000	46.0000	44.0000	54.0000	40.0000	17.0000	37.0000	49.0000	28.0000	36.0000	25.0000	34.0000	57.0000	61.0000	29.0000	43.0000
	max	173.0000	194.0000	146.0000	168.0000	171.0000	158.0000	196.0000	162.0000	139.0000	164.0000	179.0000	155.0000	161.0000	222.0000	180.0000	166.0000	226.0000	233.0000	206.0000	200.0000	174.0000	185.0000	126.0000	137.0000	129.0000	171.0000	220.0000	208.0000	225.0000	209.0000	128.0000	112.0171	194.0000	187.0000	190.0000	211.0000	288.0000	255.0000	232.0000	188.0000	269.0000	252.0000	191.0000	219.0000	212.0000	272.0000	206.0000	333.0000	340.0000	288.0000	295.0000	240.0000	246.0000	248.0000	232.0000	193.0000	190.0000
	mean	109.0975	110.2153	89.8681	96.7054	91.7913	93.5436	91.2034	92.2530	87.6804	96.8520	96.3660	84.5732	75.1668	99.8385	89.2357	93.3222	105.1115	108.5038	103.6710	100.0976	93.4649	79.8183	57.6226	63.1167	71.8033	92.6988	108.6447	95.6611	99.3708	104.9655	80.0986	81.8962	87.3143	94.4870	86.7335	110.2302	147.7827	138.0462	109.7303	105.2719	138.9024	135.3292	119.7700	131.1875	133.1860	150.1594	110.9841	166.7504	171.5197	145.4208	159.8083	134.0945	147.3728	148.0595	124.7560	109.6429	122.0000
	std	33.5981	35.9756	26.2070	27.3498	28.5154	28.0027	29.3801	31.4027	26.6178	29.4296	34.8529	26.2314	29.8660	43.9144	33.8042	33.5641	42.9618	47.1765	39.4597	41.7895	34.8083	31.6726	20.5955	18.7018	21.6651	30.2429	36.3905	34.5723	52.5089	39.7996	21.6350	22.0239	27.8635	34.5399	36.1457	48.3074	59.3378	50.3425	34.0012	31.5554	48.1052	43.4189	27.1952	37.4464	33.9139	49.7138	46.6959	57.6103	62.9317	52.4980	58.0953	46.6637	47.1658	46.6288	39.5642	35.5136	58.7258
PT08.S4(NO2)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	1134.0000	1260.0000	1158.0000	1050.0000	1076.0000	955.0000	1098.0000	1091.0000	1202.0000	1235.0000	1110.0000	1048.0000	1254.0000	1286.0000	1227.0000	1285.0000	1270.0000	1272.0000	1234.0000	1317.0000	1259.0000	1390.0000	1204.0000	1084.0000	1208.0000	1060.0000	1108.0000	1189.0000	1059.0000	1080.0000	1260.0000	1050.0000	1158.0000	1268.0000	963.0000	779.0000	697.0000	874.0000	1042.0000	787.0000	682.0000	698.0000	778.0000	940.6912	809.0000	810.0000	709.0000	657.0000	726.0000	738.0000	791.0000	551.0000	708.0000	983.0000	1043.0000	742.0000	958.0000
	max	2390.0000	2679.0000	2095.0000	2439.0000	2560.0000	2446.0000	2684.0000	2572.0000	2400.0000	2667.0000	2605.0000	2337.0000	2486.0000	2746.0000	2530.0000	2394.0000	2622.0000	2460.0000	2357.0000	2662.0000	2322.0000	2404.0000	2114.0000	1931.0000	2143.0000	2555.0000	2260.0000	2409.0000	2531.0000	2365.0000	2612.0000	2072.0000	2595.0000	2775.0000	2643.0000	2032.0000	2235.0000	2562.0000	2405.0000	2018.0000	2271.0000	1832.0000	1808.0000	1790.0000	1902.0000	2083.0000	1262.9826	1870.0000	1712.0000	1542.0000	1868.0000	1848.0000	1747.0000	2028.0000	2147.0000	2005.0000	1777.0000
	mean	1584.6275	1716.5119	1488.5952	1543.4471	1532.8688	1568.5417	1638.6488	1676.9583	1641.7798	1663.3690	1626.8929	1454.5900	1684.5952	1730.7083	1708.2599	1680.8475	1759.9167	1656.4405	1584.1905	1700.6190	1603.1298	1692.5893	1603.9775	1490.0774	1499.1718	1600.8512	1461.8185	1608.6488	1556.8214	1570.1988	1710.1369	1421.3036	1740.2381	1679.3393	1608.9405	1215.1548	1181.0238	1476.2976	1439.4702	1196.2619	1208.4137	1157.9733	1074.7370	1249.8472	1330.3214	1195.3155	879.7548	1051.5238	1088.2734	993.2143	1118.8452	959.4821	1116.2633	1292.9167	1420.1131	1144.0952	1195.0667
	std	253.7583	295.7079	213.8439	262.1349	244.7315	277.8202	307.7813	293.9112	246.4995	293.1831	264.1147	214.5271	214.0929	290.0779	221.7754	212.6782	258.9084	241.1909	217.6214	235.5518	183.9521	174.3749	164.8099	148.4322	139.3208	266.5683	175.2791	281.4597	349.5403	277.8914	291.0350	226.9915	301.4312	306.7480	366.4507	250.2112	310.9004	325.9123	288.2700	217.8347	231.8791	240.5562	170.6712	183.5437	268.1259	261.0409	126.4806	240.6183	213.9123	131.2727	197.5945	253.1675	228.1175	221.0499	237.9307	244.6727	245.5534
PT08.S5(O3)	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	384.0000	370.0000	344.0000	341.0000	320.0000	263.0000	305.0000	319.0000	343.0000	354.0000	360.0000	301.0000	445.0000	377.0000	334.0000	466.0000	427.0000	386.0000	437.0000	427.0000	393.0000	396.0000	404.0000	368.0000	456.0000	342.0000	385.0000	468.0000	382.0000	640.0000	549.0000	392.0000	568.0000	540.0000	440.0000	261.0000	296.0000	644.0000	483.0000	324.0000	387.0000	318.0000	337.0000	521.0000	463.0000	412.0000	253.0000	292.0000	337.0000	296.0000	348.0000	221.0000	262.0000	415.0000	544.0000	322.0000	489.0000
	max	1905.0000	2359.0000	1519.0000	1798.0000	1806.0000	2086.0000	1983.0000	2108.0000	1687.0000	1895.0000	2054.0000	1789.0000	2202.0000	2147.0000	1690.0000	1660.0000	2043.0000	2475.0000	1791.0000	2176.0000	1691.0000	1607.0000	1433.0000	1302.0000	1390.0000	1782.0000	2321.0000	1743.0000	1820.0000	2236.0000	2143.0000	1625.0000	2235.0000	2372.0000	2519.0000	1720.0000	2452.0000	2522.0000	2197.0000	2018.0000	2523.0000	2480.0000	2004.0000	2159.0000	1802.0000	2331.0000	1296.1468	2214.0000	2494.0000	1746.0000	1727.0000	1913.0000	2088.0000	2140.0000	2159.0000	1890.0000	1729.0000
	mean	1111.4706	1219.6607	862.0000	975.6502	894.4612	955.6071	1039.1667	1049.0298	860.2262	1040.2381	998.7798	829.3111	866.5833	967.9345	886.5883	917.1537	1024.4048	1044.0714	977.8631	1097.6310	851.5331	854.0179	753.6333	709.8869	759.3609	972.7976	993.2980	1025.3750	1007.5119	1187.7413	1241.5774	868.6845	1346.8155	1205.6429	1222.7083	855.0060	1117.5417	1503.7440	1140.2083	1026.1071	1151.6548	1224.1887	912.0268	1153.2352	1271.9345	1284.2560	630.2752	1212.5119	1144.6646	943.2202	920.8690	872.5417	1071.9753	1158.5714	1218.3333	788.1369	995.2667
	std	362.4545	395.3982	267.9472	332.4326	312.1580	386.0292	407.4759	393.8974	295.8590	349.9999	336.9261	288.3187	280.4743	348.4990	254.0365	267.5126	322.1283	436.7461	297.9020	384.9107	257.3851	244.5177	223.7792	195.1348	173.8073	325.0643	318.4881	311.1043	385.5823	349.1725	358.9085	278.1533	359.3962	369.6606	435.9667	351.1918	423.1223	446.3378	376.0609	318.1600	375.6491	532.3692	313.2340	327.9004	344.5220	476.6562	247.3312	457.0818	458.1082	345.3060	311.0878	445.5603	430.2276	384.8501	372.2695	330.6950	445.1219
T	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	6.1000	9.9000	6.3000	8.1000	7.4000	9.1000	9.5000	12.9000	7.4000	11.3000	14.9000	11.6000	16.4000	17.2000	18.3000	17.8000	20.2000	19.7000	16.2000	21.2000	20.2000	20.7000	22.4000	18.6000	19.5000	19.7000	19.1849	16.8000	12.2000	11.9000	17.1000	13.9000	12.6000	14.6000	9.9000	3.2000	1.3000	2.6000	8.3000	4.0000	2.2000	1.2000	2.1000	5.4000	2.4000	1.8000	1.0000	0.3000	2.9000	0.6000	1.4000	-1.9000	0.3000	7.2000	10.3000	8.9000	9.5000
	max	22.2000	29.3000	21.3000	27.6000	22.7000	21.5000	31.3000	28.4000	30.9000	31.5000	32.8000	32.6000	31.8000	40.6000	37.6000	42.2000	40.4000	42.6000	41.4000	44.6000	40.4000	39.3000	40.5000	39.9000	38.3000	40.7000	38.4000	35.2000	34.3000	28.9000	30.8000	24.4000	27.2000	24.9000	26.8000	21.5000	18.8000	16.8000	19.2000	20.3000	16.8000	14.9000	15.0000	16.9000	15.8000	15.8000	11.8000	15.7000	19.9000	13.8000	13.0000	14.8000	20.2000	28.8000	25.7000	30.0000	28.5000
	mean	12.4735	17.1143	12.9298	16.3741	15.5247	14.4048	18.1363	19.3083	16.4000	19.5726	22.8036	21.8494	22.7887	27.0565	25.8681	27.5034	30.3208	29.4786	27.4411	31.1625	29.6378	28.8214	30.3258	29.6411	28.0161	28.5601	26.7196	23.7685	22.5405	21.3071	23.0690	17.7946	20.9518	19.2679	19.6476	11.6560	11.8976	10.7708	13.1792	13.8345	10.1093	8.2755	9.5650	10.5553	10.0161	7.8143	4.9785	6.7310	8.2445	8.1381	5.8982	5.3387	10.5354	15.8310	17.4226	16.9470	16.9600
	std	4.1068	4.5795	3.7026	4.5561	3.8951	2.9525	5.8160	4.0352	3.7253	4.6115	4.9091	5.2302	3.9992	6.5377	4.9064	5.8770	5.5971	6.0386	6.5469	6.3539	5.4067	5.0966	4.8973	5.2503	5.0646	5.0561	4.4427	4.0305	5.0300	3.8758	3.4857	2.6777	3.4374	2.4058	3.3871	3.7562	4.0488	3.3541	2.4367	3.1609	3.0726	2.8332	2.9209	3.2415	3.3265	3.2456	2.0677	3.9796	3.4173	2.7299	2.3896	3.8535	5.1708	5.4188	3.6192	4.5581	7.0894
RH	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	28.4000	14.9000	23.1000	20.0000	18.9000	27.3000	16.2000	20.4000	19.7000	19.0000	17.1000	9.2000	22.3000	14.2000	18.8000	11.9000	12.7000	9.6000	11.8000	12.3000	13.7000	21.1000	15.9000	10.0000	15.4000	16.0000	13.8000	22.4000	23.0000	21.3000	31.8000	35.2000	43.0000	47.1000	32.1000	31.3000	14.0000	36.7000	49.1000	18.9000	16.3000	29.6000	27.5000	45.6798	30.8000	20.8000	25.9000	17.2000	20.0000	18.0000	30.6000	13.5000	14.4000	15.1000	22.8000	9.9000	13.1000
	max	81.1000	71.1000	83.2000	78.1000	80.6000	82.4000	80.5000	78.6000	85.2000	70.5000	61.6000	54.8000	82.3000	62.3000	60.8000	60.9000	59.6000	53.2000	59.8000	69.3000	63.6000	81.8000	68.0000	67.4000	66.9000	66.8000	70.4000	87.2000	76.6000	71.8000	80.5000	84.6000	78.4000	86.5000	78.1000	87.1000	76.7000	85.7000	88.7000	81.4000	84.5000	82.9000	83.5000	83.8000	86.6000	83.8000	80.4000	74.5000	85.0000	70.0000	86.6000	84.0000	80.9000	74.5000	83.6000	80.6000	63.1000
	mean	53.9480	48.9935	52.3917	45.9064	49.8732	57.4810	48.2167	48.0571	59.5018	44.6732	35.8518	32.5610	48.6970	36.3637	39.9022	35.9341	35.6970	31.2583	31.9554	34.7726	34.3085	48.3190	44.1586	37.7554	39.9565	38.8024	36.6985	52.3054	47.8577	50.7937	56.7125	59.5875	63.0071	69.9976	60.8851	60.4292	43.8536	69.0298	73.8655	50.9387	56.7870	54.9694	54.1148	61.9274	65.3905	55.8911	46.5545	44.9762	49.3517	43.1405	68.3095	47.8964	45.8875	48.8429	56.3845	47.0440	42.7867
	std	12.7451	14.0011	14.3069	14.3195	15.0211	14.0707	17.8368	15.0541	13.8906	14.0491	11.8934	12.7115	16.4059	12.8636	10.7822	12.9813	12.3616	11.9905	12.7920	13.5396	12.6837	15.3796	15.0325	12.3751	12.7067	14.0423	12.6528	14.9754	13.2462	12.4752	11.2547	12.6154	8.7083	8.1340	11.6663	13.7894	15.4792	11.4762	9.0333	16.5186	14.6960	14.9442	13.6297	8.5666	11.8126	15.2033	8.3198	14.3491	13.3080	11.6875	14.6919	17.2195	14.8886	16.3214	15.2100	17.9383	18.5104
AH	count	102.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	168.0000	15.0000
	min	0.6195	0.5237	0.5319	0.4023	0.4969	0.4868	0.5625	0.6760	0.6445	0.6686	0.5673	0.3754	0.8811	0.7502	1.0172	0.7613	0.7749	0.7526	0.7158	0.9941	0.8335	1.3863	1.0296	0.6591	0.9692	0.8162	0.8342	1.0272	0.6514	0.7773	1.3546	0.9107	1.0581	1.3156	0.6073	0.4329	0.1988	0.4412	0.8674	0.3119	0.2749	0.3340	0.3766	0.5948	0.4100	0.3422	0.2726	0.2477	0.3033	0.2269	0.3962	0.1847	0.2672	0.5782	0.6346	0.3866	0.5028
	max	0.9341	1.0945	1.0919	1.0912	1.0717	1.2695	1.2953	1.4852	1.4681	1.3250	1.2771	1.2148	1.7040	1.5020	1.4733	1.7193	1.9390	1.6308	1.4452	2.0042	1.9998	2.1806	2.1719	2.0767	1.8710	1.6872	2.2310	1.9776	1.7261	1.6261	1.8881	1.6384	1.8632	2.0224	1.9800	1.1328	1.1455	1.2700	1.3713	1.2326	1.1106	1.1381	1.0851	0.9971	1.0567	0.9972	0.6791	0.6967	1.0859	0.7413	0.7530	0.7382	0.9292	1.0250	1.3930	1.2839	0.8275
	mean	0.7558	0.9008	0.7516	0.8269	0.8399	0.9236	0.9267	1.0292	1.0755	0.9556	0.9383	0.7907	1.2721	1.1944	1.2644	1.2181	1.4338	1.1711	1.0504	1.4228	1.3310	1.7798	1.7734	1.4780	1.4320	1.3998	1.2124	1.4728	1.2768	1.2603	1.5467	1.1920	1.5390	1.5401	1.3835	0.8282	0.6146	0.9023	1.1123	0.8001	0.7107	0.6257	0.6508	0.8033	0.8090	0.5868	0.4105	0.4295	0.5414	0.4605	0.6275	0.4341	0.5751	0.8146	1.0775	0.8645	0.7248
	std	0.0816	0.0972	0.1143	0.1888	0.1364	0.1830	0.1403	0.2108	0.1799	0.1343	0.1633	0.1898	0.2195	0.1632	0.0996	0.2033	0.2492	0.1713	0.1233	0.2065	0.2844	0.1415	0.2711	0.3262	0.2233	0.2041	0.2565	0.2749	0.3113	0.3013	0.1229	0.2121	0.2014	0.1303	0.2870	0.2055	0.2587	0.2060	0.1315	0.2698	0.1723	0.2488	0.1930	0.1400	0.1790	0.1513	0.0829	0.0975	0.1655	0.1044	0.0906	0.1656	0.1824	0.1030	0.1740	0.2566	0.0978

Data Extraction

AirQualityUCI.csv

0.75MB

Description for attributes

Date (DD/MM/YYYY)
Time (HH.MM.SS)
[CO(GT)]: True hourly averaged concentration CO in mg/m^3 (reference analyzer)
[PT08.S1]: (tin oxide) hourly averaged sensor response (nominally CO targeted)
[NMHC(GT)]: True hourly averaged overall Non Metanic HydroCarbons concentration in microg/m^3 (reference analyzer)
[C6H6(GT)]: True hourly averaged Benzene concentration in microg/m^3 (reference analyzer)
[PT08.S2]: (titania) hourly averaged sensor response (nominally NMHC targeted)
[NOx(GT)]: True hourly averaged NOx concentration in ppb (reference analyzer)
[PT08.S3]: (tungsten oxide) hourly averaged sensor response (nominally NOx targeted)
[NO2(GT)]: True hourly averaged NO2 concentration in microg/m^3 (reference analyzer)
[PT08.S4]: (tungsten oxide) hourly averaged sensor response (nominally NO2 targeted)
[PT08.S5]: (indium oxide) hourly averaged sensor response (nominally O3 targeted)
[T]: Temperature in Â°C
[RH]: Relative Humidity (%)
[AH]: Absolute Humidity

Data Interpolation

Data description after interpolation through Gaussian Process(GP)

daily volatility(;standard error) and mean

cross-sectional description

	column	count	normality	l_shift	r_shift	iqr_min	iqr_25	mean	iqr_75	iqr_max	std	diff_maxmin
0	CO(GT)	9357.0	False	True	False	0.1000	1.1000	2.102615	2.800000	11.900	1.371028	11.8000
1	PT08.S1(CO)	9357.0	False	True	False	647.0000	938.0000	1097.691746	1222.000000	2040.000	213.893057	1393.0000
2	NMHC(GT)	1231.0	False	True	False	7.0000	76.0000	218.553901	297.000000	1189.000	184.403001	1182.0000
3	C6H6(GT)	9357.0	False	True	False	0.1000	4.5000	10.033281	13.700000	63.700	7.336185	63.6000
4	PT08.S2(NMHC)	9357.0	False	True	False	383.0000	736.0000	936.686728	1105.000000	2214.000	263.138532	1831.0000
5	NOx(GT)	9357.0	False	True	False	2.0000	95.0000	237.567906	322.000000	1479.000	202.292320	1477.0000
6	PT08.S3(NOx)	9357.0	False	True	False	322.0000	664.0000	834.655380	965.000000	2683.000	252.980266	2361.0000
7	NO2(GT)	9357.0	False	True	False	2.0000	73.0000	108.064926	135.000000	340.000	46.594004	338.0000
8	PT08.S4(NO2)	9357.0	False	False	True	551.0000	1216.0000	1450.059221	1665.000000	2775.000	344.348153	2224.0000
9	PT08.S5(O3)	9357.0	False	True	False	221.0000	737.0000	1021.100171	1257.000000	2523.000	392.316597	2302.0000
10	T	9357.0	False	True	False	-1.9000	11.5000	18.186668	24.300000	44.600	8.851993	46.5000
11	RH	9357.0	False	False	True	9.2000	36.2000	49.220253	61.935725	88.700	17.093713	79.5000
12	AH	9357.0	False	True	False	0.1847	0.7288	1.019927	1.306700	2.231	0.403081	2.0463

longitudinal description

	Normality					Heteroskedasticity			Autocorrelation			Stationary												Summary
	jb_stats	jb_pval	skew	kurtosis	determination	bh_stats	bh_pval	determination	lb_stats	lb_pval	determination	adf_stats	adf_pval	adf_used_lag	adf_nobs	adf_critical_value_5%	kpss_stats	kpss_pval	kpss_used_lag	kpss_critical_values_5%	adf_determination	kpss_determination	determination	Autocorrelation	Heteroskedasticity	Normality	Stationary
CO(GT)	7006.070249	0.000000e+00	1.427208	6.134064	False	1.319321	1.116028e-14	True	6672.912750	0.000000e+00	True	-10.267951	4.072187e-18	37	9319	-2.861850	1.326229	0.010000	42	0.463	True	False	False	True	True	False	False
PT08.S1(CO)	1028.166592	5.450814e-224	0.781977	3.437283	False	1.011468	7.501991e-01	False	7317.908522	0.000000e+00	True	-9.701349	1.070125e-16	38	9318	-2.861850	0.491353	0.043614	47	0.463	True	False	False	True	False	False	False
C6H6(GT)	5729.397567	0.000000e+00	1.385777	5.648389	False	0.799953	4.792266e-10	True	6584.589871	0.000000e+00	True	-10.300587	3.380466e-18	37	9319	-2.861850	0.830241	0.010000	42	0.463	True	False	False	True	True	False	False
PT08.S2(NMHC)	535.960078	4.147132e-117	0.581900	3.142361	False	0.874264	1.764749e-04	True	7051.977577	0.000000e+00	True	-10.395797	1.966836e-18	37	9319	-2.861850	1.042781	0.010000	43	0.463	True	False	False	True	True	False	False
NOx(GT)	10697.346443	0.000000e+00	1.765343	6.869386	False	7.652051	0.000000e+00	True	7695.744176	0.000000e+00	True	-6.883601	1.412917e-09	26	9330	-2.861850	9.428993	0.010000	50	0.463	True	False	False	True	True	False	False
PT08.S3(NOx)	5037.073665	0.000000e+00	1.118870	5.812869	False	0.758071	1.150333e-14	True	7695.240985	0.000000e+00	True	-10.581876	6.872173e-19	36	9320	-2.861850	3.567417	0.010000	49	0.463	True	False	False	True	True	False	False
NO2(GT)	1127.862309	1.224085e-245	0.764447	3.745229	False	2.018402	5.928394e-84	True	7619.229219	0.000000e+00	True	-7.526296	3.677213e-11	32	9324	-2.861850	8.069080	0.010000	48	0.463	True	False	False	True	True	False	False
PT08.S4(NO2)	82.452356	1.246517e-18	0.226822	3.075445	False	0.528635	9.887155e-70	True	7797.407995	0.000000e+00	True	-5.966929	1.977626e-07	37	9319	-2.861850	9.684327	0.010000	53	0.463	True	False	False	True	True	False	False
PT08.S5(O3)	653.751364	1.095708e-142	0.642244	3.164052	False	1.246734	7.685124e-10	True	7563.208040	0.000000e+00	True	-11.032393	5.625545e-20	36	9320	-2.861850	1.065825	0.010000	48	0.463	True	False	False	True	True	False	False
T	254.963898	4.318104e-56	0.323656	2.515282	False	0.264708	1.000786e-281	True	9124.195826	0.000000e+00	True	-2.883684	4.727850e-02	29	9327	-2.861850	7.578053	0.010000	55	0.463	True	False	False	True	True	False	False
RH	238.984833	1.273805e-52	-0.042656	2.221733	False	1.471940	5.276172e-27	True	8692.293601	0.000000e+00	True	-7.329900	1.135061e-10	38	9318	-2.861850	3.128120	0.010000	52	0.463	True	False	False	True	True	False	False
AH	243.143172	1.592689e-53	0.270941	2.425537	False	0.497165	3.687968e-83	True	9216.839755	0.000000e+00	True	-5.069178	1.616381e-05	25	9331	-2.861850	4.324071	0.010000	57	0.463	True	False	False	True	True	False	False
NMHC(GT)	955.878225	2.714443e-208	1.571748	5.958812	False	2.448508	4.847462e-19	True	765.148931	2.039492e-168	True	-2.937991	4.110514e-02	23	1207	-2.863938	1.176806	0.010000	16	0.463	True	False	False	True	True	False	False

Missing Value & Duplication Inspection

The number of total data is 9,357 and number of datum with missing values was counted monthly in the data.

Monthly Missing-values count aggregation

before interpolation

	column		total	missing-value				duplication
		quasi-dtypes	freq	not_freq	freq	ratio	rank	cardinality	selectivity	rank
0	CO(GT)	numeric	9357	7674	1683	0.179865	2.0	97	0.010367	1.0
1	PT08.S1(CO)	numeric	9357	8991	366	0.039115	9.0	1042	0.111360	8.0
2	NMHC(GT)	numeric	9357	914	8443	0.902319	1.0	430	0.045955	4.0
3	C6H6(GT)	numeric	9357	8991	366	0.039115	9.0	408	0.043604	3.0
4	PT08.S2(NMHC)	numeric	9357	8991	366	0.039115	9.0	1246	0.133162	10.0
5	NOx(GT)	numeric	9357	7718	1639	0.175163	4.0	926	0.098963	7.0
6	PT08.S3(NOx)	numeric	9357	8991	366	0.039115	9.0	1222	0.130597	9.0
7	NO2(GT)	numeric	9357	7715	1642	0.175484	3.0	284	0.030352	2.0
8	PT08.S4(NO2)	numeric	9357	8991	366	0.039115	9.0	1604	0.171422	11.0
9	PT08.S5(O3)	numeric	9357	8991	366	0.039115	9.0	1744	0.186385	12.0
10	T	numeric	9357	8991	366	0.039115	9.0	437	0.046703	5.0
11	RH	numeric	9357	8991	366	0.039115	9.0	754	0.080581	6.0
12	AH	numeric	9357	8991	366	0.039115	9.0	6684	0.714332	13.0

after interpolation

	column		total	missing-value				duplication
		quasi-dtypes	freq	not_freq	freq	ratio	rank	cardinality	selectivity	rank
0	CO(GT)	numeric	9357	9357	0	0.000000	7.5	1779	0.190125	8.0
1	PT08.S1(CO)	numeric	9357	9357	0	0.000000	7.5	1406	0.150262	5.0
2	NMHC(GT)	numeric	9357	1231	8126	0.868441	1.0	747	0.079833	1.0
3	C6H6(GT)	numeric	9357	9357	0	0.000000	7.5	772	0.082505	2.0
4	PT08.S2(NMHC)	numeric	9357	9357	0	0.000000	7.5	1611	0.172171	7.0
5	NOx(GT)	numeric	9357	9357	0	0.000000	7.5	2564	0.274019	12.0
6	PT08.S3(NOx)	numeric	9357	9357	0	0.000000	7.5	1587	0.169606	6.0
7	NO2(GT)	numeric	9357	9357	0	0.000000	7.5	1925	0.205728	9.0
8	PT08.S4(NO2)	numeric	9357	9357	0	0.000000	7.5	1969	0.210431	10.0
9	PT08.S5(O3)	numeric	9357	9357	0	0.000000	7.5	2109	0.225393	11.0
10	T	numeric	9357	9357	0	0.000000	7.5	802	0.085711	3.0
11	RH	numeric	9357	9357	0	0.000000	7.5	1119	0.119590	4.0
12	AH	numeric	9357	9357	0	0.000000	7.5	7049	0.753340	13.0

References

https://archive.ics.uci.edu/dataset/360/air+quality

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